Let U_n=2+2^3+2^5+ .+2^ 2 n+1 and V_n=1+4+4^2+ .+4^ n-1 . Then, _ n U_n V_n is equal to

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Correct answer: A. 8

Given, U_n=2+2^3+2^5+2^7+ +2^ 2 n+1 and V_n=1+4+4^2+ +4^ n-1 U_n= l r-a r-1 = 2^ 2 n+1 4-2 4-1 = 2^ 2 n 8-2 3 and ' V_n= l r-a r-1 = 4^ n-1 4-1 4-1 = 2^ 2 n -1 3 Now, U_n V_n = 2^ 2 n 8-2 2^ 2 n -1 = 8- 2 2^ 2 n 1- 1 2^ 2 n _ n U_n V_n = _ n 8- 2 2^ 2 n 1- 1 2^ 2 n = 8-0 1-0 =8

Let U_n=2+2^3+2^5+ .+2^ 2 n+1 and V_n=1+4+4^2+ .+4^ n-1 . Then, _ n U_n V_n is equal to

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