गणितीय आगमन से सिध्द करे `1+3+5+…….+(2n-1)=n^(2)`

Prove that n^n > 1, 3, 5,…………(2n - 1) .

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)

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)

If n is a natural number then show that 1.3.5.7…..(2n-1) = ((2n)!)/(2^n n!)

frac{(2n)!}{(1.3.5….(2n-1))n!} =

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

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