3. (a) Prove that the Root Test applied to the series 00 1 L (log k )log...

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3.

(a) Prove that the Root Test applied to the series 00 1 L (log k )log k k=2 183

(c) f (p:t·

k=1 yields r = 1. Use the Logarithmic Test to Prove that this series converges.

(b) Prove that the Ratio Test applied to the series

~ 1· 3··· (2k - 1)

L..J 4 . 6· .. (2k + 2)

k=1 yields r = 1. Use Raabe's Test to Prove that this series converges.

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