Convergency Divergency

[kangkan]

Please help with establishing the convergency or divergency of the series

1/2^p +3/2^p + 4/3^p......


2) 1+1/2^2 +2^2/3^3 + 3^3/4^4....

[Noel]

I tried to do the first series and i'm not sure about the answer i got so please do correct me if you have the answer key..does it converge for all p>2

[kangkan]

yes..thsts the ans given..an you show the steps?

[Noel]

[SoniaKapoor]

Noel...do we have to use p series here?

[Dreyfus]

@ kangkan plz post the second series .....as second term seems 2 b quite unclear....

[kangkan]

the general term i s {(n-1)^(n-1)}/n^n

[Noel]

@sonia..yes we have to use it

[Noel]

Just for confirmation..does the second series diverge for all n?

[SoniaKapoor]

ThAnkuu noel

[kangkan]

yes noel..it diverges...

[Anjali]

@ Noël , for the first ques , how did you arrive at summation 1/n^p-1 ?

[Anjali]

Also please explain the second. Isn't it approaching/converging to 0 ?

[Noel]

@anjali..notice the part 2/2^p+3/3^p+...  it can be written as 1/2^(p-1)+1/3^(p-1)+...  hence the general term 1/n^(p-1)

[Anjali]

Yeah got it ! Thanks !
What about the second one ?

[Noel]

[Noel]

There is one error in the summation in the solution above..the limit must be from 2 to infinity rather than from 0 to infinity

[kangkan]

thanks noel

[phelps.phan]

hi Noel, can u suggest some material from which these concepts(conv and divg) can be learnt

[SINGHAM]

https://class.coursera.org/sequence-002/lecture

This may help.