my teacher marked this wrong on the test

should i argue with her, or is this just wrong.

i got 0 credit for it, instructions of the test were:

"fore each of the follwoing, determine wheter the infinite series converges or diverges. if it is an alternating series, determine whether it coverges conditionally or absolutely.

she wrote on the test "geometric series converges" which i see works but how about this:

http://i176.photobucket.com/albums/w...ntitled4-1.jpg

is that mathmatically wrong somewhere?