Question

C=1+1/4+1/4^2+.....+1/4^2016

Answer 1

\(C=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{2016}}\)

\(\Rightarrow4C=4+1+\frac{1}{4}+...+\frac{1}{4^{2015}}\)

\(\Rightarrow4C-C=3C=4-\frac{1}{4^{2015}}\)

\(\Rightarrow C=\left(\frac{4^{2016}-1}{4^{2015}}\right):3=\frac{4^{2016}-1}{4^{2015}.3}\)

Answer 2

\(C=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{2016}}\)

\(4C=4+1+\frac{1}{4^2}+...+\frac{1}{4^{2015}}\)

\(3C=4C-C=4-\frac{1}{4^{2016}}\)

=> \(C=\frac{4-\frac{1}{4^{2016}}}{3}\)

Answer 3

\(C=1+\frac{1}{4}+\frac{1}{4^2}+...+\frac{1}{4^{2016}}\)

\(\Rightarrow4C=4+1+\frac{1}{4}+...+\frac{1}{4^{2015}}\)

\(\Rightarrow4C-C=4-\frac{1}{4^{2015}}\)

\(\Rightarrow3C=4-\frac{1}{4^{2015}}\)

\(\Rightarrow C=\frac{4^{2016}-1}{4^{2015}.3}\)