Prove be mathematical induction :
`(1)/(3.6)+(1)/(6.9)+(1)/(9.12)+...+(1)/(3n(3n+3))=(n)/(9(n+1))`

Prove that by using the principle of mathematical induction for all n in N : (1)/(2.5)+ (1)/(5.8) + (1)/(8.11)+ ...+(1)/((3n-1)(3n+2))= (n)/(6n+4)

Prove that by using the principle of mathematical induction for all n in N : (1)/(1.4)+ (1)/(4.7)+(1)/(7.10)+...+ (1)/((3n-2)(3n+1))= (n)/(3n+1)

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) .

Prove that by using the principle of mathematical induction for all n in N : (1)/(3.5)+ (1)/(5.7)+ (1)/(7.9)+ ....+(1)/((2n+1)(2n+3))= (n)/(3(2n+3))

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))

Prove that 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)

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) .

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

Prove by induction that (1)/(1*3)+(1)/(3*5)+(1)/(5*7)+ . . .+(1)/((2n-1)(2n+1))=(n)/(2n+1)(ninNN) .

Prove by mathematical induction 1^(2)+2^(2)+3^(2)+.....+(n+1)^(2)=((n+1)(n+2)(n+3))/(6)