By the alternating series test, the series converges. Find its sum. First find the partial fraction decomposition of 5 k(k+ 10) Then find the limit of the partial sums. 5( − 1) k+1 k(k + 10) k=1 = 5( − 1) k + k(k + 10) k=1 5 k(k + 10)

By the alternating series test, the series converges. Find its sum. First find the partial fraction decomposition of 5 k(k+ 10) Then find the limit of the partial sums. 5( − 1) k+1 k(k + 10) k=1 = 5( − 1) k + k(k + 10) k=1 5 k(k + 10)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.6: Partial Fractions

Problem 58E: Match the rational expression on the left with the correct partial fraction decomposition form on...

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Question

5.1

By the alternating series test, the series
converges. Find its sum.
First find the partial fraction decomposition of
5
k(k + 10)
Then find the limit of the partial sums.
k+1
∞
k = 1
=
5( − 1)k
k(k + 10)
=
5( − 1)k+
k(k + 10)
k=1
5
k(k + 10)

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Similar questions

Match the rational expression on the left with the correct partial fraction decomposition form on the right. x2-2x+3x2x-4x2+5 a. Ax+Bx2+Cx3+Dx4+Ex-4+Fx+Gx2+5 b. Ax+Bx-4+Cx-42+Dx-43+Fx+Gx2+5+Hx+Ix2+52 c. Ax+Bx2+Cx-4+Dx2+Ex+Fx3+5 d. Ax+Bx2+Cx3+Dx-4+Ex-42+Fx+Gx2+5 e. Ax+Bx-4+Cx+Dx2+5 f. Ax+Bx2+Cx-4+Dx+Ex2+5
Can you explain why a partial fraction decomposition is unique? (Hint: Think about it as a system of equations.)
Can you explain how to verify a partial fraction decomposition graphically?

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