Let F(x) (x 1) ln(1 x) x (a) Apply integration to the result of Exercise 49 to prove that for 1 (b) Evaluate at x 1 2 to prove (c) Use a calculator to verify that the partial sum S 4 approximates the left hand side with an error no greater than the term a5 of the series 3 In 2 3 2 1 2 1 2 2 1 2 1 2 3 2 1 3 4 24 1 4 5 25

Question: Let F(x) = (x + 1) ln(1 + x) x. (a) Apply integration to the result of Exercise 49 to prove that for 1

Let F(x) = (x + 1) ln(1 + x) − x.

(a) Apply integration to the result of Exercise 49 to prove that for −1

(b) Evaluate at x = 1/2 to prove

3 In 2 3/2 - 1|2 1 = 2 1.2.2 1 2.3.2 + 1 3.4.24 1 4.5.25 (c) Use a calculator to verify that the partial sum S₄approximates the left-hand side with an error no greater than the term a5 of the series.

3 In 2 3/2 - 1 = 2 1.2.2 1|2 1 2.3.2 + 1 3.4.24 1 4.5.25

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