Question

an example of convergent and not increasing sequence , please?

Answer 1

Consider, \[\left\{ s_n \right\} = \frac{1}{n^2}\]. This is the sequence 1, 1/4, 1/9, 1/16, ...

Answer 2

Thanks :)

Answer 3

can you give me an example of zero sequences, their sums diverge ?

Answer 4

As in a sequence that converges to zero, but whose sum diverges? I would think 1/n would be a good choice: 1/1, 1/2, 1/3, 1/4, ... the sum of this sequence (shockingly) turns out to be infinite!