23\sqrt{1 + \frac{1}{n^{2}}+ \frac{1}{(n+1)^{2}}}
=\sqrt{\frac{n^{2}+1 }{n^{2}} + \frac{1}{(n+1)^{2}}}
=\sqrt{\frac{(n+1)^{2}-2n }{n^{2}} + \frac{1}{(n+1)^{2}}}
=\sqrt{\frac{[(n+1)^{2}-2n][n+1]^{2} + n^{2}}{n^{2}(n+1)^{2}}}
=\sqrt{\frac{(n+1)^{4}-2n[n+1]^{2} + n^{2}}{n^{2}(n+1)^{2}}}
=\sqrt{\frac{[(n+1)^{2}- n]^{2}}{n^{2}[n+1]^{2}}}
=\frac{(n+1)^{2}-n}{n(n+1)}
=\frac{n+1}{n} - \frac{1}{n+1}
=1 +\frac{1}{n}-\frac{1}{n+1}
now u can solve
