For the following telescoping series, find a formula for the nth term of the sequence of partial sums {S,}. Then evaluate lim S, to obtain the value of the series or state that the series diverges. 10 (5k - 1)(5k + 4) k= 1 Sn

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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For the following telescoping series, find a formula for the nth term of the sequence of partial sums {S,}. Then evaluate lim S, to obtain the value of the series or state
that the series diverges.
10
(5k - 1)(5k + 4)
k= 1
Sn
Transcribed Image Text:For the following telescoping series, find a formula for the nth term of the sequence of partial sums {S,}. Then evaluate lim S, to obtain the value of the series or state that the series diverges. 10 (5k - 1)(5k + 4) k= 1 Sn
Evaluate the series E
2k
3
two ways as outlined in parts (a) and (b).
2k+1
k= 1
3
a. Evaluate E
3
using a telescoping series argument.
2k 2k+1
k=1
3
b. Evaluate E
3
3
using a geometric series argument after first simplifying
3
by obtaining a common denominator.
2k 2k+1
k= 1
2k 2k+1
a. Write the nth term in the enumeration of the partial sum.
3
Sn
3
3
3
3
+
+
+...+
(Type an exact answer.)
2' 22
23
23 24
Transcribed Image Text:Evaluate the series E 2k 3 two ways as outlined in parts (a) and (b). 2k+1 k= 1 3 a. Evaluate E 3 using a telescoping series argument. 2k 2k+1 k=1 3 b. Evaluate E 3 3 using a geometric series argument after first simplifying 3 by obtaining a common denominator. 2k 2k+1 k= 1 2k 2k+1 a. Write the nth term in the enumeration of the partial sum. 3 Sn 3 3 3 3 + + +...+ (Type an exact answer.) 2' 22 23 23 24
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