hw1 - x n 1 = 3 x n 2 x n 2 Prove that x n> 2 for all n...

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(1) Prove that 1 1 · 2 + 1 2 · 3 + ... 1 n ( n + 1) = n n + 1 (2) Prove that 1 2 + 2 2 2 + 3 2 3 + ... + n 2 n = 2 - n + 2 2 n (3) Prove that 1 + 2 q + 3 q 2 + ... + nq n - 1 = 1 - ( n + 1) q n + nq n +1 (1 - q ) 2 (4) Find the sum of the following geometric progression x 1 + x 2 + x 2 (1 + x 2 ) 2 + ... + x n (1 + x 2 ) n (5) Prove that 1 2 + 3 2 + ... + (2 n + 1) 2 = ( n + 1)(2 n + 1)(2 n + 3) 3 (6) Let x 1 > 2. Define x n by the formula
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Unformatted text preview: x n +1 = 3 x n +2 x n +2 Prove that x n > 2 for all n . Extra Credit Problem (to be written up and submitted separately) Find the formula for the sum 1 4 + 2 4 + ... + n 4 1...
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