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

Question

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

anonymous · Answer

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

anonymous · Answer

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

sirm3d · Answer

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

zepp · Answer

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

anonymous · Answer

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

anonymous · Answer

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, ...

zepp · Answer

Um, I see, thanks!