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Solved: Telescoping series For the following telescoping
Chapter 11, Problem 48E(choose chapter or problem)
47-58. Telescoping series For the following telescoping series, find a formula for the nth term of the sequence of partial sums \(\left\{S_{n}\right\}\). Then evaluate \(\lim_{n\rightarrow\infty}\ S_n\), to obtain the value of the series or state that the series diverges.
\(\sum_{k=1}^{\infty}\left(\frac{1}{k+2}-\frac{1}{k+3}\right)\)
Questions & Answers
QUESTION:
47-58. Telescoping series For the following telescoping series, find a formula for the nth term of the sequence of partial sums \(\left\{S_{n}\right\}\). Then evaluate \(\lim_{n\rightarrow\infty}\ S_n\), to obtain the value of the series or state that the series diverges.
\(\sum_{k=1}^{\infty}\left(\frac{1}{k+2}-\frac{1}{k+3}\right)\)
ANSWER:Step1
Given that
Step2
To find
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evalua