Question

For the following telescoping series, find a formula for the nth term of the sequence of partial sums ($S_n$). Then evaluate $\lim_{n \to \infty} S_n$ to obtain the value of the series or state that the series diverges.\\ $\sum_{k=1}^{\infty} \frac{4}{(4k-1)(4k+3)}$ $S_n = \boxed{} Select the correct choice and fill in any answer boxes in your choice below. A. $\sum_{k=1}^{\infty} \frac{4}{(4k-1)(4k+3)} = \boxed{}$ (Simplify your answer.) B. The series diverges.

          For the following telescoping series, find a formula for the nth term of the sequence of partial sums ($S_n$). Then evaluate $\lim_{n \to \infty} S_n$ to obtain the value of the series or state that the series diverges.\\
$\sum_{k=1}^{\infty} \frac{4}{(4k-1)(4k+3)}$
$S_n = \boxed{}
Select the correct choice and fill in any answer boxes in your choice below.
A. $\sum_{k=1}^{\infty} \frac{4}{(4k-1)(4k+3)} = \boxed{}$ (Simplify your answer.)
B. The series diverges.

For the following telescoping series, find a formula for the nth term of the sequence of partial sums (Sn). Then evaluate limn →∞ Sn to obtain the value of the series or state that the series diverges.

∑k=1^∞(4)/((4k-1)(4k+3))
Sn =
Select the correct choice and fill in any answer boxes in your choice below.
A.∑k=1^∞ (4)/((4k-1)(4k+3)) = (Simplify your answer.)
B. The series diverges.

Added by Santiago M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

04/26/2023

Step 1

Step 1: We are given the telescoping series 85, 4, 4k+1/(4k+3), k=2 to infinity. Show more…

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thanks! For the following telescoping seriesfind a formula for the nth term of the sequence of partial sums {S}Then evaluatelim S to obtain the value of the series or state that the series diverges 85 4 4k1(4k+3 k21 S Select the correct choice and fill in any answer boxes in your choice below BThe series diverges.