Calculus 1 problem: series

[Pliskinus]

Im doing some older exams that my professor has provided, but I havent got the solutions for this one. Can someone help confirm that the solution Ive arrived at is correct? Since both problems are related to series, I hope its not an issue that I post them together.

 

[Deleted member 4993]

Im doing some older exams that my professor has provided, but I havent got the solutions for this one. Can someone help confirm that the solution Ive arrived at is correct? Since both problems are related to series, I hope its not an issue that I post them together.

View attachment 19317

View attachment 19318

Please tell us the "steps" you took to arrive at the location of the solution.

 

[Steven G]

Do you know what radius means? Do you know that exponential equations grow faster than cubic equations?

If you radius of convergence is 1, then -1<x<1 and so 0<x+1<2. 2^n/n^3 gets fairly LARGE when n gets large. So therefore 2^n/n^3 and (-1)^2*2^n/n^3 will naturally converge, correct?

 

[HallsofIvy]

I could always circle "D Don't Know" and they would have to mark it correct!