Question:

A)

and

Find the radii of convergence of these series and show that

and

for all

B)

For every

, let

denote the function:

show that

has constant value

C)

Use this result or by another means to show that for all

Solution:

It is difficult for me to write it out on here because I don't know how to write all the maths properly like everybody else on maths forum because I am new!

but for A) I think I must be going wrong because for both

and

the ratio test is telling me they are both null series and thus they converge for all

. Is this correct?

b) I am unsure how to begin this part, maybe i need to use part a)

any advice would be good as I'm having trouble even really starting this question!

Thank you.