Question

How to do \[\large \sum_{k=2}^{5}(-1)^{k+1}2^{k-1}\]
Is there a way to simplify this?

Answer 1

There are only 4 numbers to add. It's probably best just to do it all.

Answer 2

(-1)^(k+1) just decides if the term will be positive or negative though...

Answer 3

we'll give a hint. the first term is negative

Answer 4

I know that I could easily add them by hand -.- But I want to know if I could simplify this

Answer 5

\[\sum_{k=1}^4(-1)^k2^k\]

Answer 6

You want to simplify at least one of the k+1 or k-1 indexes in the sum, since there's not really any reason for them both to be skewed like that. And (-1)^something is pretty easy to change into anything else... and you know it goes 2^1, 2^2, ...

Answer 7

Um, I see, thanks!