Here's a Power Seires Problem?

Question

Determine the interval of convergence of the series sum of 4/3*(-1)^k*x^k/(k+7)^(1/7) as k goes from 1 to infinity.
Below a is the left endpoint of the interval of convergence and b is right endpoint of the interval of convergence. ak is the kth term of the power series, e.g., ak=ck * x^k is the series is sum of ck * x^k as k goes from 1 to infinity.Enter the absolute value of t as abs(t). 
A geometric series has terms c*r^k with r > 0 and r not = 1. A p-series has terms k^p with p not = 0.

one of the questions is :
(a) Find abs(a(k+1)/ak)         (k is kth terms, is not a number or varible, it is a subcase, but I cannot type subcase here)

The problem is I don't get what is "a" ... it is the left endpoint of the interval of convergence of sum of 4/3*(-1)^k*x^k/(k+7)^(1/7) as k goes from 1 to infinity, or the sum of ck * x^k as k goes from 1 to infinity??? and what is "t"... and what are geometric and p series doing here?? I'm totally confused... anyone can help me?

Alam Ko Iyan · Accepted Answer

if you observe.. the interval of convergence is..
(-1 , 1].

at x = -1... the series is a p-series... and its is divergent...

at x = 1, it is an alternating series... and convergent...

otherwise... it has a geometric form...
so from [a, b=1] the series is convergent...

so... letting... a be a number r whose absolute value is less than 1  |r| < 1
then
|a(k+1)/ak| = |r| (k+8 / k+7)^1/7 ... i think this is what is intended here...



§

Anonymous · Answer

particularly situations no count how useful and helpful your approach is a pair of particular difficulty; the ability of the difficulty will nevertheless outweigh the ability of suggestion. (suggesting to your self that no longer something is incorrect whilst there is something incorrect)

Here's a Power Seires Problem?

2 Answers