extra credit hw viii

2 lim 1 3 m 2 2 lim m 4 3 5 2 6 5 7 2m

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Unformatted text preview: ing the summation symbol: ∞ 1 2 (5) . n=1 The series in (4) is convergent divergent Check one Give proof in the next page. Use the following, if necessary: ⋆ Wallis’ product formula. 2 lim 1 ·3 m− ∞ → = 2 2 · lim m− ∞ → 4 3 ·5 2 · 6 ··· 5 ·7 2m !! ·√ 2m − 1 !! 5 2 2m 2m − 1 2m + 1 1 2m + 1 2 = π . 2 . Proof. 6 (6) Know that, for x with x > 0, I x 1 Ix = u=0 Evaluate this integral I x 1 x in (0) is expressed as u2 − · u2 − x−1 x x+1 x 2 du. directly . Use the following information, if necessary: “Let a and b be constants, with a > 1. Then an antiderivative of fu u2 − b = 2 u2 − a is Fu (7) = a−b 2a u a − u2 − a+b √ 4a a ln Use the result of (6) to evaluate the series in (4). Show work for (6) and (7). Attach a separate sheet. 7 √ ” a +u √ . a −u...
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This note was uploaded on 01/12/2014 for the course MATH 116 taught by Professor Scholle,minho during the Fall '08 term at Kansas.

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