Hi! Can someone help me figure out these problems please? I have to determine whether the series converge or diverge and give a reason to the answer. Thanks!

1.)

∞

Σ [ln (n+1)]/(n+1)

n=2

2.)

∞

Σ 2/ (1+e^n)

n=1

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- Feb 5th 2006, 03:40 AMcherry106converge or diverge problem
Hi! Can someone help me figure out these problems please? I have to determine whether the series converge or diverge and give a reason to the answer. Thanks!

1.)

∞

Σ [ln (n+1)]/(n+1)

n=2

2.)

∞

Σ 2/ (1+e^n)

n=1 - Feb 5th 2006, 04:26 AMCaptainBlackQuote:

Originally Posted by**cherry106**

as it is just the tail of the harmonic series.

RonL - Feb 5th 2006, 04:34 AMCaptainBlackQuote:

Originally Posted by**cherry106**

RonL - Feb 6th 2006, 12:59 AMcherry106
Thanks for the help!

For problems like that how do you know what to compare the equation to? for example in question one you compared the denominator to {1}/{n+1} for n>e-1 and for question two you used n^2 for n>0. - Feb 6th 2006, 03:34 AMCaptainBlackQuote:

Originally Posted by**cherry106**

thing decreases more slowly that 1/(n+1) so we try comparing the series with

the harmonic series.

In the second we have essentially 1/(1+e^n), but e^n increases more

rapidly than any power of n, so 1/(1+e^n) decreases more rapidly than

the reciprocal of any power of n, and as

$\displaystyle \sum 1/n^2$

is the first of these series which converges its what we use for a comparison

series.

RonL