MAC 2312 Midterm: MAC2312 C06 Test 4
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Instructions: write your complete solutions on your answer paper. No graphing calculators are allowed to be used. You are not required to simplify your answers. (1) (20 pts. ) For the following, determine whether the series converges or di- verges. For each convergent series, nd the sum. (a) (c) For the following, determine whether the series converges abso- lutely, converges conditionally, or diverges. (a) (b) Xn=0 ( 1)n+1(n 1) n2 + n + 3 ( 1)n(n) n + 1 (c) Xn=1 ( 1)n ln n n2 (3) (30 pts. ) For each power series, nd the interval of convergence. (a) Xn=1 xn+1 (n 1)! (4) (10 pts. ) = 1 + x + x2 + x3 + . on the interval ( 1, 1). (a) find a power series for z (b) using the answer to (a), approximate z 0. 1 dx. 1 + x5 to within 10 10. (5) (10 pts. )
