$$ ext { If }\left(1+\frac{3}{1} ight)\left(1+\frac{5}{4} ight)\left(1+\frac{7}{9} ight) \ldots\left(1+\frac{2 n+1}{n^2} ight)=121 ext {, } $$ then $n=$

Question

$$ 	ext { If }\left(1+\frac{3}{1}ight)\left(1+\frac{5}{4}ight)\left(1+\frac{7}{9}ight) \ldots\left(1+\frac{2 n+1}{n^2}ight)=121 	ext {, } $$ then $n=$

Aicharya · Accepted Answer

We have, $ \begin{array}{ll} \left(1+\frac{3}{1}ight)\left(1+\frac{5}{4}ight)\left(1+\frac{7}{9}ight) \ldots\left(1+\frac{2 n+1}{n^2}ight)=121 \ \Rightarrow \quad 	ext { (4) }\left(\frac{9}{4}ight)\left(\frac{16}{9}ight) \ldots\left(\frac{n^2+2 n+1}{n^2}ight)=121 \ \Rightarrow n^2+2 n+1=121 \Rightarrow(n+1)^2=121 \ \Rightarrow n+1=11 \Rightarrow \quad n=10 \end{array} $

$$ \text { If }\left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right)…

Solution