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>> SPEAKER 1: Let's write a program that
prompts the user for a positive

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integer, n, and then prints out
the sum of all the numbers

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between 1 and n.

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Well, here we have main, which I've
already written in advance.

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And notice here at the top of
main, I declare an int n.

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>> I then, inside of a do while
loop, first print out

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positive integer, please.

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Then I proceed to get an integer from
the user with the CS50 library's get

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int function.

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And then in my while condition here, I
make sure that n is greater than or

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equal to 1 before I actually proceed
to do something with that value.

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>> What do I do next?

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Well, I call a function that I'm going
to call sigma, representative of the

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capital sigma that you might have
recalled from math classes that

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indicates that you want to sum something
from one value to another.

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And whatever that function returns as
its return value, I'm going to store

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in a variable called answer.

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>> Finally, in my last line in main, I'm
going to print out what answer is.

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Of course, we haven't yet implemented
this function sigma.

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So how do we go about doing that?

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>> Well, at the bottom of my file, I'm
going to proceed to declare a function

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that returns an int.

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And I'm going to call
that function sigma.

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And I'm going to specify that as input
that function accepts also an int.

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And I'll call it just, to be
distinct, m instead of n.

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But we could have called it the
most anything we'd like.

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>> Inside of the body of this function I'm
going to proceed to use a familiar

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construct, namely a loop.

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But I'm also going to do a bit of sanity
checking to make sure that the

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user doesn't provide me with a number
that I'm not expecting.

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In particular, I'm going to do if m is
less than 1 and, somewhat arbitrarily,

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I'm simply going to return 0 if
the number is not a positive

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integer as I expect.

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>> Then I'm going to declare a variable
called sum and initialize it to 0.

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This will ultimately store the sum of
all of the numbers between 1 and m.

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And then I'm going to use a familiar
forward loop construct.

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For int i gets 1, i is less than
or equal to m, i plus plus.

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And then, within the body of this
loop, I'm simply going to do sum

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equals sum plus i.

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Or, more simply, sum plus equals i,
which achieves the same result.

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>> And then lastly, I need to return
the sum that I've computed.

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So I add in return sum.

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>> Now I'm not done yet.

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I need to teach C that this
function actually exists.

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And so atop my file I'm going to declare
what we've called a function

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prototype, identical to the signature
that I used when defining the function

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a moment ago.

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>> Specifically, just above main,
I'm going to type int

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sigma, int m, semicolon.

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Not implementing the function
again, simply declaring it.

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If I now save, compile, and run this
program, let's see what I get.

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Make sigma 0 dot slash sigma 0.

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And now let's provide a positive integer
like 2, which should give me

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three, because the values between
1 and 2 are 1 plus 2 equals 3.

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And indeed, that's what I get.

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>> Let's run it again, this
time with, say, 3.

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So I should get 1 plus 2 plus
3 should give me 6.

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And indeed, I do get 6.

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>> And let's try one last value, say 50.

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And 1,275 is our answer.

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