Greetings,

I am currently enrolled in a Finite Math course in college and let me tell you...

My professor ~~sucks~~ is just not good at explaining the material. He's not a bad human being like 99% of my class portrays him to be, but teaching is just not his strongest point.

With that in mind, I've been assigned homework and did all of it but one question - which I do not even recall learning about in class.

The question goes:

*Compute the following sums given that the integer π is an even number 2π.*

a. π = ( π ) + ( π ) + ( π ) + β― + ( π )

______( 0 )___( 2 )___( 4 )______( 2m )

b. π = ( π ) + ( π ) + ( π ) + β― + ( π )

______( 1 )___( 3 )__( 5 )_____( 2m-1 )

I absolutely have no idea how to approach this question... The previous math course I took was Pre-Calculus.

However, I would greatly appreciate if somebody could either give me an example of a solution (doesn't have to be this problem) or some other source which explains how to approach this problem, so I could learn how to do it.

Thank you for your time!

## Couscous_Knight

I'm very confused as to what S is in both a and b.

For a), do you mean Sm = sum_{ k = 0 to m} 2*k ? (adding all even integers from 0 to 2*m)

For b), do you mean Sm = sum_{ k = 0 to m} (2*k - 1) ? (adding all odd integers from 0 to 2*m-1)

## etzpcm

I think it's meant to be sums of binomial coefficients. Can /u/Loliliker0108 confirm?

## Couscous_Knight

Ooooh, right, that makes waaay more sense.

## Loliliker0108

yes, your guess is correct. It should be something like for example ( n over 0 without a dividing line)

## Couscous_Knight

In that case, I assume you know what (a+b)

^{n}is ?## Loliliker0108

Yes, I am aware of binomial expansion, where (a+b)^n would be (a+b)(a+b)(a+b)...(a+b) for the n-times. If that's what you are asking at least...

## Couscous_Knight

I meant do you know what the expansion is written as a sum which involves the binomial coefficient

(a+b)

^{n}= sum_{k=0 to n} (choose k from n) a^{n-k}b^{k}If you use this sum for the right a and b (twice, so you get a system of equations involving both the Sa and Sb (ie the sum over k even and odd)), you should get your answer.

Can you think of such a and b ?