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Unformatted text preview: R 1 x 2 +4 x +5 dx is completing the square. If f is continuous and lim x →∞ f ( x ) = 0 then R ∞ 1 f ( x ) dx converges. If f is even and R ∞ f ( x ) dx converges, then so does R ∞∞ f ( x ) dx . If a n converges, then lim a na n1 = 0. The harmonic series converges to zero. If ∑ a n converges to S then the sequence of its partial sums converges to S . The series 11 + 11 + 11 + . . . converges to 0. Every increasing sequence that is bounded above converges. BONUS (5 pts) Compute the sum of the series 1 / 2+2 / 4+3 / 8+4 / 16+ . . . . Hint: it is not geometric or telescoping, so it is not easy. But it is related to the series 1 / 2+1 / 4+1 / 8+ . . . . 4...
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 Summer '08
 Storfer
 Calculus, Arc Length, dx, good first step

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