Prove by the method of induction
`(1)/(1*2)+(1)/(2*3)+(1)/(3*4)+…………` upto n terms `=(n)/(n+1)` where `n in N`

Using the principle of mathematical induction prove that 1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)++1/(1+2+3++n)=(2n)/(n+1) for all n in N

Using the principle of mathematical induction prove that 1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)++1/(1+2+3++n)=(2n)/(n+1) for all n in N

Using the principle of mathematical induction , prove that for n in N , (1)/(n+1) + (1)/(n+2) + (1)/(n+3) + "……." + (1)/(3n+1) gt 1 .

Show that the middle term in the expansion of (1+ x)^(2n) is (1.3.5…(2n-1) )/( n!). 2^(n) . x^(n) , where n in N .

Using the principle of mathematical induction, prove that 1/(1*2)+1/(2*3)+1/(3*4)+…+1/(n(n+1)) = n/((n+1)) .

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

Using mathematical induction, prove that (1)/(1.3.5) + (2)/(3.5.7) +….+(n)/((2n-1)( 2n+1) ( 2n+3)) =( n(n+1))/( 2(2n+1) (2n+3))

Prove that the term independent of x in the expansion of (x+1/x)^(2n) \ is \ (1. 3. 5 ... (2n-1))/(n !). 2^n .

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

Using mathematical induction prove that 1/(n+1)+1/(n+2)+……+1/(2)gt13/24AAn in N and n gt1