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Now up to this point,

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we've only been using for loops in association with lists.

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So we've been looping through the list and getting hold of each of the items in

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the list and then doing something with it, right?

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But we're not always going to be working with lists and using for loops.

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Sometimes we might want to use a loop completely independent of a list.

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And a good example of this is when Carl Gauss the German

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mathematician was just a child when he was 10 years old,

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his math teacher gave him an exercise that she probably thought would tie him up

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for it a little while.

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And the idea was to get him to add all of the numbers from 1 to 100.

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So 1 + 2 + 3 + 4 + 5, et cetera,

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all the way until a hundred.

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And even though she thought this would keep him busy for an hour or so getting

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this young child to add up these numbers and I can have some peace and quiet

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scrolling on Facebook,

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but unfortunately he came back to her within two minutes and gave her the

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answer. So how did he work it out? Well,

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here's actually a really smart kid and he figured out that if you flip the

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numbers around, so 100 + 99 + 98,

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and you'll look at both of these two lines,

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you can see that 1 + 100 = 101, 2

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+ 99 = 101, 3 + 98 = 101, basically,

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if you tie all of these numbers together,

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there's actually 50 pairs of 101.

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So he could simply just do 50 multiplied by 101 which is 5,050.

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And that's how he figured out the answer.

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But we can actually outshine Gaus because we can do this calculation in less

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than a minute, just by writing a few lines of code. But in order to do this,

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we first have to learn about using for loops with the range function.

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Now the range function is something that is really, really helpful

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if you want to generate a range of numbers to loop through.

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And the syntax looks something like this.

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So we've still got our for and our in keywords highlighted in blue,

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but instead of looping through a list,

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we define how our loop is going to work by creating a range.

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So in this case,

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I'm creating a range between a and b and then I'm going to get hold of each

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number in that range and do something with that number.

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So for example, if I wrote for number in range,

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and then my range is going to be 1, 10.

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So this is going to be the range that I'm going to create between 1 and 10

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and then I want to get hold of each of the numbers inside that range.

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And this is going to be between 1 and 10 and not including 10.

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So if I go ahead and print out the number that I create from my for loop,

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then you'll see that what happens is it prints 1 2 3 4 5 

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6 7 8 9, but not the last digit, which I've included here.

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So if I wanted all of the numbers from 1 to 10,

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I actually have to set a range between 1 and 11.

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And now when you run the code,

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you can see that it goes from 1 all the way up to 10.

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Now by default,

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the range function will step through all the numbers from the start to the end,

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and it will increase by 1. Now,

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if you want it to increase by any other number,

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then you have to add another comma to the end of it and specify how large you

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want the step to be. So let's say we changed the step size to three.

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Now, if I rerun the same code,

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you'll see that it goes from one and then it steps by three to four and then it

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steps by three. And then it steps by three, finally to 10.

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Now let's come back to the problem that I mentioned at the beginning of this

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lesson.

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How can we add up all of the numbers from 1 to 100 by using code?

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Well,

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it's going to involve a for loop and it's going to involve the range function

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because we're going to get hold of every number in the range between 1 and

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100,

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so we need to write 101. Once we've got hold of all of these numbers,

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it's as simple as using a accumulator,

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so let's say a total = 0. And then inside the for loop,

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so that means indented,

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we're going to say total += number.

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So now it's going to add every number in this range to the total starting from

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zero.

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And this is basically going to give us the sum of every number from 1 to 100.

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So let's go ahead and print it out and see if it matches Gauss's value.

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And there you have it 5,050.

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So now that we've beaten Gauss at his own game of math using programming,

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let's head over to the next lesson and try to complete a challenge using the

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range function to see if you managed to internalize and understand everything we

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talked about in this lesson. So for all of that and more, I'll see you there.