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The A.M of the observations 1.3.5,3.5.7,...

The A.M of the observations `1.3.5,3.5.7,5.7.9,...,(2n-1)(2n+1)(2n+3)` is

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

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

1.3+2.4+3.5+....+n(n+2)=(n(n+1)(2n+7))/(6)

Prove that by using the principle of mathematical induction for all n in N : 1.3+3.5+5.7+....+(2n-1)(2n+1)= (n(4n^(2)+6n-1))/(3)

Prove that by using the principle of mathematical induction for all n in N : 1.3+3.5+5.7+....+(2n-1)(2n+1)= (n(4n^(2)+6n-1))/(3)

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

Prove by mathematical induction. 1/1.3+1/3.5+1/5.7+....+1/((2n-1)(2n+1))=n/(2n+1)

By the Principle of Mathematical Induction, prove the following for all n in N : 1/1.3+1/3.5+1/5.7+......+ 1/((2n -1)(2n +1))= n/(2n +1) .

Prove by mathematical induction that 1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n+1)) = n/(2n+1),(n in N)