5. Σ cosh -1 6. Σ n=2 logn n 7. Σ πιο +1) nlog(n+1) n=1 n=2...

Question

Question

5. Σ cosh -1 6. Σ n=2 logn n 7. Σ πιο +1) nlog(n+1) n=1 n=2

8.Σ (n!)?(2η)!(3n51 - 43n10)18 η (3η)! nel

math calculus

Answer 1

Answer #1

(5)

Solution: cosh -1 x-1 Apply Series Integral Test: - Check if f(n)ispositive, continuous and decreasing cosh - lis positive, c

1 = V= =-- -adu ---9--- du 12 (-Ei(u)) Substitute backu = - 72 4(+18) 72 = e *x+Ei Jedin 1 Apply u-substitution :u=-

( - CC -1-1 = -18 1 E- 2 2 = dn = (-radio = - erredia () a -= e -dra Apply Integration By Parts: v1 (e) =e PE (-1)-1 (-) (m)

1 Substitute backu 72 = - -Ei 72 cein-E: ) Therefore, Compute the boundaries: salonte:(+)e*r-si() ==+*+=(+4)*-s(3)+c (x)dx= F

Answer 2

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