Question

Tính nhanh 

\(M=\frac{1+2+2^2+2^3...+2^{2012}}{2^{2014}-2}\)

Answer 1

\(M=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}\)

\(=>2M=\frac{2+2^2+2^3+2^4+...+2^{2013}}{2^{2014}-2}\) 

\(=>M=\frac{\left(2+2^2+2^3+2^4+...+2^{2013}\right)-\left(1+2+2^2+2^3+...+2^{2012}\right)}{2^{2014}-2}\)

\(=>M=\frac{2^{2013}-1}{2^{2014}-2}\)

Answer 2

https://coccoc.com/search/math#query=%5B(2%5E2013)-1%5D%2F%5B(2%5E2014)-2%5D%5D

Answer 3

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