# Thread: can anyone give me two more examples?

1. ## can anyone give me two more examples?

I am struggling to understand infinte series can anyone give me two more examples?

2. Originally Posted by jameyt
I am struggling to understand infinte series can anyone give me two more examples?

$\sum_{n=1}^\infty 1-(\frac{1}{n})^\frac{1}{n}$

which diverges and can be seen defining the function:

$f(x) = 1-(\frac{1}{x})^\frac{1}{x} - \frac{1}{x}$

for x > 10, and seeing that it is always positive which would mean

$\frac{1}{n}$ is a lower bound ( when n is bigger than 10).

but :

$\sum_{n=1}^\infty (-1)^n (1-(\frac{1}{n})^\frac{1}{n})$

converges due to Leibniz criteria.