" 34."1+(1)/(4)+(1)/(9)+(1)/(16)+...+(1)/(n^(2))<2-(1)/(n)" for all "n>=2,n in N

Prove that 1+(1)/(4)+(1)/(9)+(1)/(16)+....+(1)/(n^(2)) 2,n in N

If quad lim_(n rarr oo)(1-(1)/(4))(1-(1)/(9))(1-(1)/(16))...(1-(1)/(n^(2)));n>=1 then (1)/(P) is equal to

(1)/(2)+(1)/(4)+(1)/(8)+(1)/(16)+......+(1)/(2^(n))=1-(1)/(2^(n))

lim_(n rarr oo) ((1)/(1.2) + (1)/(2.3) + (1)/(3.4) +…..+ (1)/(n(n+1))) is :

Let P(n) : 1+ (1)/(4) + (1)/(9) + …. + (1)/(n^2) lt 2 - (1)/( n) is true for

Using Mathemtical induction, show that for any natural number n, (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))=(n)/(n+1)

For all ngt=1 , prove that , (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + ……+ (1)/(n(n+1)) = (n)/(n+1)

For all quad prove that (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))=(n)/(n+1)

By using the principle of mathematical induction , prove the follwing : P(n) : (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …….+ (1)/(n(n+1)) = (n)/(n+1) , n in N