Wednesday, 18 July 2018

calculus - How to solve the limit of this sequence $lim_{n to infty} left(frac{1}{3cdot 8}+dots+frac{1}{6(2n-1)(3n+1)} right)$

$$\lim_{n \to \infty} \left(\frac{1}{3\cdot 8}+\dots+\frac{1}{6(2n-1)(3n+1)} \right)$$
I have tried to split the subset into telescopic series but got no result.
I also have tried to use the squeeze theorem by putting the $a_n$ between $\frac{1}{(2n-1)(2n+1)}$ and $\frac{1}{(4n-1)(4n+1)}$ but it doesn't work.

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