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Question Number 31461 by abdo imad last updated on 08/Mar/18

l e t g i v e u_{n} = \sum_{k = 1}^{n} s i n (\frac{k}{n}) s i n (\frac{k}{n^{2}})

1) p r o v e t h a t t h e s e q u e n c e (u_{n}) i s c o n v e r g e n t

2) f i n d {l i m}_{n \to \infty} u_{n} .