Rewrite the series Sigma^infinity_k = 2 3^k + 1/4^k in the form of a geometric s

Question

Rewrite the series Sigma^infinity_k = 2 3^k + 1/4^k in the form of a geometric series and apply the geometric series formula to evaluate it Please explain. I have a big test tomorrow morning Do not copy and paste from Wolfram. Please handwrite and write quite legibly for everyone to read. Write very legibly and neatly so that it is easy to read out and understand. Do not let the edges of a scanned or pictured image are cropped, resulting illegible scripts. Do not skip steps. Never use the multiply symbol (times) between numbers and letters. I need solutions and answers as soon as possible. Many thanks.

Explanation / Answer

Let S=3^(k+1)/4^k from to 2.

So, S=(3^3/4^2)+(3^4/4^3)+(3^5/4^4)+________________+

a=3^3/4^2=27/16

r= (3^4/4^3)/(3^3/4^2)=3/4

S=a/(1-r)

S=(27/16)/(1-3/4)

S=(27/16)*4

S=27/4 Ans.

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