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
In question one we have something slowly increasing over n+1, so the wholeOriginally 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
is the first of these series which converges its what we use for a comparison
series.
RonL