( 1 + \frac { 3 } { 1 } ) ( 1 + \frac { 5 } { 4 } ) ( 1 + \frac { 7 }

1.	( 1 + \frac { 3 } { 1 } ) ( 1 + \frac { 5 } { 4 } ) ( 1 + \frac { 7 } { 9 } ) \dots ( 1 + \frac { 2 n + 1 } { n ^ { 2 } } ) = ( n + 1 ) ^ { 2 }
Answer» (1+3/1)(1+5/4)(1+7/9).... (1+2n+1/n²)= 4/1(9/4)(16/9)*(25/16).....((n²+2n+1)/n²).. here all the denominator will cancel its earlier numerator terms like 4 and 4, 9 and 9 , leaving behind the numerator of last term so, at last it will become (n²+2n+1)/1 = (n+1)²

( 1 + \frac { 3 } { 1 } ) ( 1 + \frac { 5 } { 4 } ) ( 1 + \frac { 7 } { 9 } ) \dots ( 1 + \frac { 2 n + 1 } { n ^ { 2 } } ) = ( n + 1 ) ^ { 2 }

Answer»

(1+3/1)(1+5/4)(1+7/9).... (1+2n+1/n²)= 4/1*(9/4)*(16/9)*(25/16).....((n²+2n+1)/n²)..

here all the denominator will cancel its earlier numerator terms like 4 and 4, 9 and 9 , leaving behind the numerator of last term

so, at last it will become (n²+2n+1)/1 = (n+1)²