Thread: approximate sum of series.

Determine wheter the series is convergent or divergent. If it convergent, approximate the sum of the series correct to four decimal places.

heres the equation: http://img251.imageshack.us/img251/2261/46755781zg9.png

= alternating geometric series,

Would it be okay to move the exponent k over everything? in other words: ( (-1)/k) )^k

So then it looks alot like a geometric series, so then It converges by the rules of an alernating series, it is decreasing and it is approaching zero.

So then to find its sum, i would do so by geometric series right?

first term would be starting at k = 2, so: 1/2?

then use 1/2 divided by 1 -r

need help finding r, would it also be 1/2.

this is my best attempt right now for how to approach this problem.

Originally Posted by rcmango

Determine wheter the series is convergent or divergent. If it convergent, approximate the sum of the series correct to four decimal places.

heres the equation: http://img251.imageshack.us/img251/2261/46755781zg9.png

= alternating geometric series,

Would it be okay to move the exponent k over everything? in other words: ( (-1)/k) )^k

So then it looks alot like a geometric series, so then It converges by the rules of an alernating series, it is decreasing and it is approaching zero.

So then to find its sum, i would do so by geometric series right?

first term would be starting at k = 2, so: 1/2?

then use 1/2 divided by 1 -r

need help finding r, would it also be 1/2.

this is my best attempt right now for how to approach this problem.

you don't have a geometric series here, not really. the alternating series test will work here as well

Alright, but when the problem indicated to find the sum, i believed this only to be done through a series like a geometric?

help me to find the sum please.