Using the principle of mathematical induction prove that `1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)++1/(1+2+3++n)=(2n)/(n+1)` 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/(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

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

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 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 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. 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 : the 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)/(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

Prove the following by using the principle of mathematical induction for all n in N 1+(1)/((1+2)) + (1)/((1+2+3)) + …… + (1)/(1+2+3+…..+n) = (2n)/(n+1)