Question

find the sum of the series ∑ (x^n+1)/(n+1)

Answer 1

help me

Answer 2

n from 0 to inf ?
And also what is x ?

Answer 3

is that\[\sum_{n=0}^\infty \frac{x^{n+1}}{n+1}\]?

Answer 4

yes

Answer 5

are you sure about your question? what do they want? finding sum of series or convergence radius or something?

Answer 6

yes...very sure....

Answer 7

So its like x + x^2 /2 + x^3 /3 ....
Looks like taylor expansion for e^x . Just the slightest of manipulations

Answer 8

well \(e^x\) series is\[\sum_{n=0}^\infty \frac{x^{n}}{n!}\]

Answer 9

Oh lol i am sorry :P

Answer 10

ratio test will give you the interval \(|x|<1\) as convergence radius but I'm not sure about the sum in that interval, let's work on it :-)

Answer 11

ok...

Answer 12

@RadEn @ganeshie8 idea?

Answer 13

oh no, wait a min

Answer 14

if \(|x|<1\) you can write\[\frac{1}{1-x}=1+x+x^2+...\]take integral of both sides

Answer 15

nice :)

Answer 16

@ferwanz am I clear? :-) tnx @ganeshie8

Answer 17

yep.... tq everyone...