Question

Telescoping Series: find formula for nth term of sequence of partial sums Sn. Evaluate lim n approaches infinity Sn to obtain value of the series or state it diverges

Answer 1

\[\sum_{k=1}^{\infty} \frac{ 1 }{ 4k^2+4k-3 }\]

Answer 2

got it too
\[\frac{ 1 }{ (2k+3)(2k-1) }\]

Answer 3

did this series
\[\frac{ 1 }{ 2 }\sum_{k=1}^{\infty}(\frac{ 1 }{ 2k-1 } - \frac{ 1}{ 2k+3 })\]

Answer 4

i got an answer of -1/2 but i dont think thats right