(a) Show that the following identity is true 1 1 2n +1 n2 (n+ 1)² n²(n + 1)² (b) Use the identity in part (a) to find the formula for the nth partial sum of the series 2n +1 n²(n + 1)² n=1 (c) Use the formula for the nth partial sum obtained in part (b) to determine the convergence or divergence of the series 00 Σ n²(n + 1)² ` 2n +1 n=1
(a) Show that the following identity is true 1 1 2n +1 n2 (n+ 1)² n²(n + 1)² (b) Use the identity in part (a) to find the formula for the nth partial sum of the series 2n +1 n²(n + 1)² n=1 (c) Use the formula for the nth partial sum obtained in part (b) to determine the convergence or divergence of the series 00 Σ n²(n + 1)² ` 2n +1 n=1
Chapter8: Sequences, Series,and Probability
Section8.1: Sequences And Series
Problem 9ECP: For the series i=1510i find (a) the fourth partial sum and (b) the sum. Notice in Example 9(b) that...
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![(a) Show that the following identity is true
1
1
2n +1
n?
(n+1)²
n2(n + 1)2
(b) Use the identity in part (a) to find the formula for the nth partial sum of the series
2n +1
п? (п + 1)2
n=1
(c) Use the formula for the nth partial sum obtained in part (b) to determine the convergence or divergence of the series
2n +1
n²(n+ 1)2
n=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F519d4492-8e4c-4b4b-b1f5-a1d5c4f0934c%2F919912c2-4e32-43c0-aebe-d46cd96c054f%2Fgo43xaa_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Show that the following identity is true
1
1
2n +1
n?
(n+1)²
n2(n + 1)2
(b) Use the identity in part (a) to find the formula for the nth partial sum of the series
2n +1
п? (п + 1)2
n=1
(c) Use the formula for the nth partial sum obtained in part (b) to determine the convergence or divergence of the series
2n +1
n²(n+ 1)2
n=1
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