Prove that `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)/(n^(2))lt2-(1)/n,(ngt1)

Using mathematical induction prove that 1/(1.4)+1/(4.7)+1/(7.10)+.......+1/((3n-2)(3n+1))=n/(3n+1) for all n in N

Using mathematical induction prove that (1+3/1)(1+5/4)(1+7/9)......(1+(2n+1)/n^2)=(n+1)^2 for all n in N

Using mathematical induction prove that 1/(3.5)+1/(5.7)+1/(7.9)+.......+1/((2n+1)(2n+3))=n/(3(2n+3) for all n in N

If nge2 is an integer, prove by induction that, 1+(1)/(4)+(1)/(9)+ . . .+(1)/(n^(2))lt2-(1)/(n) .

By method of induction, prove that 1.6 + 2.9 + 3.12 +... +to n terms = n(n +1 )(n+2) for all n in N .

For all nge1 , prove that 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)

Prove the following by using the principle of mathematical induction for all n in N 1+1/4+1/9+1/16+…….+(1)/(n^2) lt 2 - 1/n, n gt= 2