Does the following series absolutely converge, conditionally converge or diverge? \sum_{n=1}^{+\infty}\sin(n^2)\sin(\frac{1}{n^2})

Dachpunkt4cr

Dachpunkt4cr

Answered question

2022-02-25

Does the following series absolutely converge, conditionally converge or diverge?
n=1+sin(n2)sin(1n2)

Answer & Explanation

Malaika Ridley

Malaika Ridley

Beginner2022-02-26Added 6 answers

Comparison works !
sin(1n2)1n21 for n. Hence there is N such that
sin(1n2)2n2 for nN. Therefore
|sin(n2)sin(1n2)|2n2 for n>N

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