Use any test for convergence/divergence to show that the series converges. V12(-1)" 3" (2n + 1) 00 (Ь) It is possible to show that the sum of the series > is T, in other words, the series n=0 converges to the number T. (You do NOT need to prove this, but it can be done somewhat easily using a Taylor series expansion of arctan x.) Suppose you want to use a partial sum of this series to estimate the value of T to an accuracy of within 0.0001. Would using the first 8 terms of the series be enough to ensure you get an accuracy of within 0.0001? (8 terms means the terms where n = 0, 1, 2, 3, ...., 7.)

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