For all `ninNN`, prove by principle of mathematical induction that,
`1+(1)/(1+2)+(1)/(1+2+3)+ . . .+(1)/(1+2+3+ . . .+n)=(2n)/(n+1)`.

Similar Questions

Explore conceptually related problems

For all ninNN , prove by principle of mathematical induction that, 1+3+5+ . . .+(2n-1)=n^(2) .

For all ninNN , prove by principle of mathematical induction that, (1)/(1*2)+(1)/(2*3)+(1)/(3*4)+ . . .+(1)/(n(n+1))=(n)/(n+1) .

For all ninNN , prove by principle of mathematical induction that, 15^(2n-1)+1 is divisible by 16.

For all ninNN , prove by principle of mathematical induction that, (1)/(2)+(1)/(4)+(1)/(8)+ . . .+(1)/(2^(n))=1-(1)/(2^(n)) .

For all ninNN , prove by principle of mathematical induction that, 2^(3n)-1 is divisible by 7.

For all ninNN , prove by principle of mathematical induction that, (1-(1)/(2))(1-(1)/(3))(1-(1)/(4)) . . .(1-(1)/(n+1))=(1)/(n+1) .

For all ninNN , prove by principle of mathematical induction that, 1*1!+2*2!+3*3!+ . . .+n*n ! =(n+1)!-1 .

For all ninNN , prove by principle of mathematical induction that, (1)/(1*4)+(1)/(4*7)+(1)/(7*10)+ . . . to terms =(n)/(3n+1) .

For all ninNN , prove by principle of mathematical induction that, 1*2+2*3+3*4+ . . . +n(n+1)=(1)/(3)n(n+1)(n+2) .

For all ninNN , prove by principle of mathematical induction that, 1^(2)+3^(2)+5^(2)+ . . .+(2n-1)^(2)=(n)/(3)(4n^(2)-1) .