The A.M. of the observations `1. 3 .5 ,3 .5 .7 ,5 .7 .9 , ....... ,(2n-1)(2n+1)(2n+3)` is `(AA n in N)`

1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)

Prove 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1), AA n in N

Find the sum 1 xx 3 xx 5 + 3 xx 5 xx 7 + 5 xx 7 xx 9 + ……. + (2n - 1) ( 2n + 1) ( 2n + 3)

Prove that 1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Prove the following by the method of induction for all n in N : 1/1.3 + 1/3.5 + 1/5.7+...+ 1 / ((2n-1)(2n+1)) = n / (2n+1)

By method of induction prove that 1.3 + 2.5 + 3.7 +...+ n (2n + 1) = n/6 (n + 1) (4n + 5) for all n in N

For all nge1 , prove that 1/1.3+1/3.5+1/5.7+......+1/((2n-1)(2n+1))=n/(2n+1)

Prove by the method of induction, (1)/( 1.3) + (1)/( 3.5) + (1)/( 5.7) + . . . + (1)/( (2n - 1)(2n + 1)) = (n)/(2 n +1)

Using mathematical induction prove that 1/(3.5)+1/(5.7)+1/(7.9)+.......+1/((2n+1)(2n+3))=n/(3(2n+3) for all n in N