A serious series problem

Calculus Level 4

Determine if the series converges, diverges or if it has no limit.

∑ n = 1 ∞ [ sin ⁡ ( n ) ] n \sum_{n=1}^{\infty} \ [ \ \sin (n) \ ]^n

Oscillating behaviour Converges Diverges

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Andrea Palma by Andrea Palma , 46, Italy

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1 solution

Aman Rajput
May 18, 2021

lim ⁡ n → ∞ ( sin ⁡ n ) n = ( → − 1 to 1 ) → ∞ \lim_{n\to\infty}(\sin n)^n = (\to -1 \; \text{to}\; 1)^{\to \infty} is oscillating and is not zero so, the series is divergent

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