I am struggling to understand infinte series can anyone give me two more examples?
Please see attachment:
$\displaystyle \sum_{n=1}^\infty 1-(\frac{1}{n})^\frac{1}{n}$
which diverges and can be seen defining the function:
$\displaystyle f(x) = 1-(\frac{1}{x})^\frac{1}{x} - \frac{1}{x}$
for x > 10, and seeing that it is always positive which would mean
$\displaystyle \frac{1}{n}$ is a lower bound ( when n is bigger than 10).
but :
$\displaystyle \sum_{n=1}^\infty (-1)^n (1-(\frac{1}{n})^\frac{1}{n})$
converges due to Leibniz criteria.