Convert the following products into factorials: (iii) `(n + 1) (n +2) (n + 3).... (2n)` (iv) `1.3.5 . 7 . 9.... (2n-1)`

Convert the following products into factorial: 1.3.5.7.9(2n-1)

Convert the following products into factorial: (n+1)(n+2)(n+3)(2n)

Convert the following products into factorial: 1. 3. 5. 7. 9 (2n-1)

Convert the following products into factorial: (n+1)(n+2)(n+3).......(2n)

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)

Prove the following by using the principle of mathematical induction for all n in N : 1/(3. 5)+1/(5. 7)+1/(7. 9)+...+1/((2n+1)(2n+3))=n/(3(2n+3)) .

Prove the following by using the principle of mathematical induction for all n in N :- 1/3.5+1/5.7+1/7.9+...+1/((2n+1)(2n+3))=n/(3(2n+3)) .

Prove the following by using the principle of mathematical induction for all n in N : (1+3/1)(1+5/4)(1+7/9)...(1+((2n+1))/(n^2))=(n+1)^2

Prove the following by using the principle of mathematical induction for all n in N :- (1+3/1)(1+5/4)(1+7/9)...(1+((2n+1))/n^2)=(n+1)^2.

Prove that ((2n)!) / (n!) = 2^n(2n - 1) (2n - 3) ... 5.3.1.