I've got in my assignment to show if the following series converges or diverges.
∞∑n=1(e1n−1−1n)
Attempt:
∞∑n=1(e1n−1−1n)=∞∑n=1(1+1n+12!n2+13!n3+...−1−1n)=∞∑n=1(12!n2+13!n3+...)=∞∑n=1(1n+12!n2+13!n3+...)
At this point I'm lost. I tried using D'Alambert as follows:
lim
which I tried to simplify with basic limit laws (hopefully correctly):
\lim\frac{\sqrt[n+1]{e}-1}{\sqrt[n]{e}-1} = 1
I don't know where to go from here. Thank you for all your help in advance.
No comments:
Post a Comment