`1/(n-1)-10/(n+2)=3`

If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1)/(2n^(2))+(1)/(3n^(3))-……) then lambda=

If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1)/(2n^(2))+(1)/(3n^(3))-……) then lambda=

Prove the following by the principle of mathematical induction: (1)/(1.4)+(1)/(4.7)+(1)/(7.10)++(1)/((3n-1)(3n+2))=(n)/(3n+1)

If n be a positive integer such that n<=3, then the value of the sum to n terms of the series 1.n-((n-1))/(1!)(n-1)+((n-1)(n-2))/(2!)(n-2)-((n-1)(n-2)(n-3))/(3!)(n-3)+dots

Find the value of 1/(81^n)-(10)/(81^n)C_1+(10^2)/(81^n)C_2-(10^3)/(81^n)C_3++(10^(2n))/(81^n) .

Find the value of 1/(81^n)-(10)/(81^n)^(2n)C_1+(10^2)/(81^n)^(2n)C_2-(10^3)/(81^n)^(2n)C_3++(10^(2n))/(81^n) .

Find the value of (1)/(81^(n))-(10)/(81^(n))^(2n)C_(1)+(10^(2))/(81^(n))^(2n)C_(2)-(10^(3))/(81^(n))^(2n)C_(3)+...+(10^(2n))/(81^(n))

Find the value of 1/(81^n)-(10)/(81^n)^(2n)C_1+(10^2)/(81^n)^(2n)C_2-(10^3)/(81^n)^(2n)C_3++(10^(2n))/(81^n)

The value of (1)/(81^(n))-(10)/(81^(n)).""^(2n)C_(2)-(10^(3))/(81^(n)).""^(2n)C_(3)+…+((10)^(2n))/(81^(n)) is

The sum of the series 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+…..+1/((n-1)!1!) is = (A) 1/(n!2^n) (B) 2^n/n! (C) 2^(n-1)/n! (D) 1/(n!2^(n-1)