$$4\sum_{k=0}^{\infty}(-1)^{k}/2k+1$$ please help

Question

anonymous · Answer

clarification please.

is the question (-1)^k/(2k)  +  1   or

is the question (-1)^k/(2k+1) ?

anonymous · Answer

only the -1 is in parenthesis the 2k +1 is not

anonymous · Answer

no. Is the entire bottom term part of the denominator or does the + 1 stand alone outside the division? That is my question.

anonymous · Answer

the +1 stands alone

anonymous · Answer

Are you sure? if the question was (-1)^k/(2k+1)  the answer is pi and the whole question is very simple. However, if the question is (-1)^k/(2k) + 1, the the math becomes difficult and the answer ends up being complex infinity. I think the first one is what your after to be honest.

anonymous · Answer

the problem on my sheet says that the one stands alone reviewing the question you appear to be correct

anonymous · Answer

what class is this for? What level and what is the name?

anonymous · Answer

this is a sheet to test us on what we know it is not relevant to the class

anonymous · Answer

Well to be honest if you are in high school i would say it is probably a mistake and they meant to include 1 in the denominator, making the answer pi. If you in college and taking higher level math classes then i would just show how the system continuously grows to complex infinity.