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## Homework Statement

Ʃ cos(k*pi)/k from 1 to infinity.

This is a test for convergence.

and when is the proper time to use the alternating series test

like using it on (-1)

^{k}(4

^{k}/8

^{k}) would result to divergence

since lim of (4

^{k}/8

^{k}) is infinity and not 0 but the function is really

convergent by the geometric series?

## Homework Equations

## The Attempt at a Solution

Is it right to do this:

for k is odd cos is negative and for k is even cos is positive

then

cos(k*pi)\k < (-1)

^{k}/k

and by alternating series test ;

(-1)

^{k}*(1/k) since 1/k is decreasing and lim as 1/k approaches infinity is 0 then

(-1)

^{k}1/k converges thus cos(k*pi)/k converges by direct comparison test.

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