when i develop the series of a cosine i have a (-1) member

i wanted to represent the series as a sum

so i need to take only the odd members so the power of -1 is 2k+1 i got

but the solution says that the power of -1 is equal

is it the same??

why they have such an expression

(they use n istead of k)

http://i45.tinypic.com/6sszue.jpg

how they got the power?