[" EXAMPLE "4," 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 1+2+3+4+…n= (n(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

Use principle of mathematical induction to prove that (1+(3)/(1))(1+(5)/(4))...(1+(2n+1)/(n^(2)))=(n+1)^(2)

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

By using the principle of mathematical induction , prove the follwing : P(n) : (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …….+ (1)/(n(n+1)) = (n)/(n+1) , 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)

Use principle of mathematical induction to prove that: 1+2+3+……….+n=(n(n+1))/2

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

Prove that by using the principle of mathematical induction for all n in N : (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))