9. Determine whether the series is absolutely convergent, conditionally convergent, or divergent. ∞ (2) Σ sin n = 1 ∞ (b

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9. Determine whether the series is absolutely convergent, conditionally convergent, or divergent. ∞ (2) Σ sin n = 1 ∞ (b) Σ n = 3 cos (n π) n sin tan Inn 3n
8. Which of the below series are convergent? 2n² n! 1. Σ n=1 z. 8 Σ n=1 cos(ηπ/3) n! L. (-1)" n=2 (Inn)" Σ ∞ v. Σ (tan In)" n = 1 8 c. Σ n = 1 n10100" n!
7. Find the real value of p for which the series is convergent. n+ √ln (n") 1+n² n=2
6. Let the series (a) Show that (b) Show that 80 n = 1 n = 1 n = 1 an is convergent. (an+1-an) is convergent. 2an 1-an is convergent.
5. The sequences {a} and {b} satisfies following conditions (i) 0 <an<bn (ii) b is convergent n = 1 then does the series converge or not? Justify your answer. Σ n = 1 1-cosbn an