determine if the series converge or diverge using an appropiate test.
∞
? 2^n - 5^n+1
n=1 6^n
.
I will show that the series converges by the integral test :
.
We thus have the integral converges . We therefore have by the integral test that the series also
.
We also have :
The series is thus the sum of three geometric series which converge :
----
and
; so , the series converges to :
.
-----
and
; so , the series converges to :
.
-----
and
; so , the series converges to :
. We thus have the series is the sum of three convergent geometric series :