Question

discuss the convergence of sequence where
=(1/4+1) +(1/4^2+1) +(1/4^3+1) .....(1/4^n+1)

Answer 1

@BSwan @ganeshie8

Answer 2

I suppose n->infinity

Answer 3

yup

Answer 4

it does not converge because of the plus one, essentially you have geometeric squenence of 1/4^n, which does converge, but the plus one to each term makes it inifinitly large, with an infininte number of plus ones, no convergence

Answer 5

\(\large X_n = \sum_{n=1}^{n} \frac{1}{4^n} +1 \)

Answer 6

so how do a theoreticaly prove it

Answer 7

I*

Answer 8

\(\large X_n = \sum_{n=1}^{n} \frac{1}{4^n} +\sum_{n=1}^{n} 1 \)

Answer 9

\(\large X_n = \sum_{n=1}^{n} \frac{1}{4^n} + n \)

Answer 10

\(\large \lim X_n =\lim \sum_{n=1}^{n} \frac{1}{4^n} +\ lim n \)

Answer 11

\(\large \lim X_n = C +\lim n \)

Answer 12

but lim n goes to + infinite

Answer 13

so does not converge

Answer 14

thanks ^^ again :P

Answer 15

sry for laging :P
so it not converge also not bounded hehe
but its tend to infinity :D
np , YW :)