" 5."2+6+18+...+2.3^(n-1)=(3^(n)-1)

Using the principle of mathmatical induction, prove each of the following for all n in N 2+6+18+…+2*3^(n-1)=(3^(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)/(2.5)+ (1)/(5.8) + (1)/(8.11)+ ...+(1)/((3n-1)(3n+2))= (n)/(6n+4)

1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)

1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))

Prove that 1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))

1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))

lim_ (n rarr oo) (2.3 ^ (n + 1) -3.5 ^ (n + 1)) / (2.3 ^ (n) + 3.5 ^ (n)) =

Using the mathematical induction, show that for any natural number n, 1/2.5 + 1/5.8 + 1/8.11 + …+ 1/((3n-1)(3n+2))=n/(6n+4)