Question

Series of square roots

Answer 1

\[\sum_{n=1}^{\infty}\frac{ \sqrt{2n+1}-\sqrt{2n-1} }{ \sqrt{4n^2-1} }\]

Answer 2

telescoping again ?

Answer 3

tried but no solution

Answer 4

factor the denominator and split the fraction

Answer 5

@ganeshie8 thx

Answer 6

yw! you can split like that because both 2n-1 and 2n+1 are > 0 for n >=1

Answer 7

it is sequences and series @Nnesha

Answer 8

see https://www.khanacademy.org/math/integral-calculus/sequences_series_approx_calc/calculus-series/v/telescoping-series

Answer 9

yes calcII