" 14."(1+(1)/(1))(1+(1)/(2))(1+(1)/(3))...(1+(1)/(n))=(n+1)

Let a_(1)=1,a_(n)=n(a_(n-1)+1 for n=2,3,... where P_(n)=(1+(1)/(a_(1)))(1+(1)/(a_(2)))(1+(1)/(a_(3)))...*(1+(1)/(a_(n))) then Lt_(n rarr oo)P_(n)=

prove that (1-(1)/(2^(2)))(1-(1)/(3^(2)))(1-(1)/(4^(2)))(1-(1)/(n^(2)))=(n+1)/(2n) for all natural numbers,n>=1(1-(1)/(n^(2)))=(n+1)/(2n)

For all quad prove that (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))=(n)/(n+1)

For all ngt=1 , prove that , (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + ……+ (1)/(n(n+1)) = (n)/(n+1)

lim_(n rarr oo)(1+(1)/(3)+(1)/(3^(2))+.......+(1)/(3^(n-1)))/(1+(1)/(2)+(1)/(2^(2))+.....+(1)/(2^(n-1)))

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)

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)

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)

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)