If `ninNN`, then by principle of mathematical induction prove that,
`7+77+777+ . . .` to n terms `=(7)/(81)(10^(n+1)-9n-10)`.

By mathematical indcution prove that, 4+44+444+ . . . "to n terms "=(4)/(81)(10^(n+1)-9n-10) .

If ninNN , then by principle of mathematical induction prove that, 1+2+3+....+nlt(1)/(8)(2n+1)^(2) .

If ninNN , then by principle of mathematical induction prove that, 3^(2n+2)-8n-9 is divisible by 64.

If ninNN , then by princuple of mathematical induction prove that, 2+222+22222+ . . .+22 . . .{(2n-1)"digits"}=(20)/(891)(10^(2n)-1)-(2n)/(9) for all positive integers n.

For all ninNN , prove by principle of mathematical induction that, 2^(2)+5^(2)+8^(2)+ . . . to n terms =(n)/(2)(6n^(2)+3n-1) .

For all ninNN , prove by principle of mathematical induction that, a+(a+d)+(a+2d)+ . . . to n terms =(n)/(2)[2a+(n-1)d] .

If ninNN , then by principle of mathematical induction prove that, 5^(2n+2)-24n-25 is divisible by 576.

By using the Principle of Mathematical Induction, prove the following for all n in N : 7+77+777 +........ to n terms = 7/81 (10^(n+1)-9n-10) .

7 + 77 + 777 + …. N terms =

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