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)

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

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

By the principle of mathematical induction prove that the following statements are true for all natural numbers 'n' (a) (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+......+(1)/((2n-1)(2n+1)) =(n)/(2n+1) (b) (1)/(1.4)+(1)/(4.7)+(1)/(7.10)+......+(1)/((3n-2)(3n+1)) =(n)/(3n+1)

Prove that ((2n+1)!)/(n !)=2^n{1. 3. 5 .........(2n-1)(2n+1)}

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

Prove the following by the principle of mathematical induction: \ 7^(2n)+2^(3n-3). 3^(n-1) is divisible 25 for all n in Ndot

By the principle of mathematical induction prove that for all natural number 'n' the following statement are true : (a) 2+4+6+........ +2n =n (n+1) (b) 1+4+7+.......+(3n-2) =1/2 n (3n-1) (C) 1^(3)+2^(3)+3^(3) +..........+n^(3)=1/4 n^(2)(n+1)^(2)