Using the principle of mathematical induction, prove that `1.3 + 2.3^(2) + 3.3^(2) + ... + n.3^(n) = ((2n-1)(3)^(n+1)+3)/(4)` for all `n in N`.

Using principle of mathematical induction, prove that 1 + 3 + 3^(2) + … 3^(n-1) = (3^(n) - 1)/(2)

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

Using the principle of mathematical induction, prove that 1.2+2.3+3.4+......+n(n+1)=(1)/(3)n(n+1)(n+2)

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), n in N

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

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

By the principle of mathematical induction prove that 3^(2^(n))-1, is divisible by 2^(n+2)

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

Using the principle of mathematical induction prove that 1/(1. 2. 3)+1/(2. 3. 4)+1/(3. 4. 5)++1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2) for all n in N