How can we prove that :

(1 + 1 / 3) (1 + 5 / 4)(1 + 7 / 9)........{(1 + (2n + 1 / n²)} = (n + 1)² for all n Є N.

Please answer this question!!!!!!!!!!

hi dude iam arjun of class 11 from chennai,seee

first (n=1)

i.e, 1+(2.1+1)/1^{2 _{= (1+1)2}}

      1+3                 =2²

       4             =          4 so p(n)=1 is true

now n=k

             (1 + 1 / 3) (1 + 5 / 4)(1 + 7 / 9) ...... 1+(2.k+1)/k^2 ₌ (k+1)^₂       keep this as - 1

now n=k+1

               1+(2(k+1)+1)/(k+1)² _{= (k+2)}²

=(1 + 1 / 3) (1 + 5 / 4)(1 + 7 / 9)……1+(2(k+1)+1)/(k+1)² _{= (k+2)}²

 (1 + 1 / 3) (1 + 5 / 4)(1 + 7 / 9)……(1+(2k+3)/(k+1)²) = (k+2)²

 (1 + 1 / 3) (1 + 5 / 4)(1 + 7 / 9)……(1+(2k+1)/(k)²) (1+(2k+3)/(k+1)²) = (k+2)² --

using 1