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Given :
(1)3+(2)3²+(3)3³+...+(n)3^n =[(2n-1)(3)^(n+1) +3]/4
To find:
Prove that by using the method Mathematical Induction ?
Solution :
Given that :
(1)3+(2)3²+(3)3³+...+(n)3^n =[(2n-1)(3)^(n+1) +3]/4
Put n = 1 then
(1)3¹ = [{(2×1)-1}(3)^(1+1)
=>3 =[(2-1)(3)²+3]/4
=> 3 = ((1)9+3)/4
=> 3 = 12/4
=> 3 = 3
This statement is true for n = 1
Now,
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