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

Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n-1))(2) Check P(1) is true.

Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n)-1)(2) If P(k) is true, prove that P(k+1) is true.

Using the principle of mathematical induction, prove that 1.3 + 2.3^(2) + 3.3^(2) + ... + n.3^(n) = ((2n-1)(3)^(n+1)+3)/(4) for all n in N .

Using the principle of mathematical induction, prove that 1.3 + 2.3^(2) + 3.3^(2) + ... + n.3^(n) = ((2n-1)(3)^(n+1)+3)/(4) for all n in N .

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

The sum of the series (2)/(3)+(8)/(9)+(26)/(27)+(80)/(81)+ to n terms is n-(1)/(2)(3^(-n)-1)(b)n-(1)/(2)(1-3^(-n))(c)n+(1)/(2)(3^(n)-1)(d)n-(1)/(2)(3^(n)-1)

Find the value of (3^n × 3^(2n + 1))/(3^(2n) × 3^(n - 1))

(2.3^(n+1)+7.3^(n-1))/(3^(n+1)-2((1)/(3))^(1-n))=

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