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tutorial_8 - Tutorial 8 1 Let x1 = 2 xn 1 = √ 3 2 xn n...

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Unformatted text preview: Tutorial 8 November 17, 2011 1. Let x1 = 2, xn+1 = √ 3 + 2 xn , n ∈ N . Prove that it converges, and calculate the limit. 2. Prove that n xn = k=1 sin (k !) k (k + 1) 3. Calculate the sum of ∞ 1 (3n − 2)(3n + 1) n=1 4. Calculate the limit of the follwing series ∞ 1 1 −n 2n 3 n=1 ∞ √ √ √ n+2−2 n+1+ n n=1 5. Test the convergence of the series, ∞ n+1 2n n=1 6. Test the convergence n+3 √ (−1) n n+4 n=1 ∞ 1 ...
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