Question

[vũ hương thảo]

tính tổng S =

    1 + 2 + 2^{2 +} 2³ + ....... + 2²⁰¹⁷

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                1 - 2²⁰¹⁸

Answer 1

[Wall HaiAnh]

\(S=1+2+2^2+2^3+...+2^{2017}\)

\(2S=2\left(1+2+2^2+2^3+...+2^{2017}\right)\)

\(\Rightarrow2S=2+2^2+2^3+2^4+...+2^{2018}\)

\(\Rightarrow2S-S=\left(2+2^2+2^3+2^4+...+2^{2018}\right)-\left(1+2+2^2+2^3+...+2^{2017}\right)\)

\(\Rightarrow S=2^{2018}-1\)

Vậy \(S=2^{2018}-1\)

Answer 2

[Nguyễn Phương Uyên]

\(S=\frac{1+2+2^2+2^3+...+2^{2017}}{1-2^{2018}}\)    (1)

đặt \(A=1+2+2^2+2^3+...+2^{2017}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2018}\)

\(\Rightarrow2A-A=\left(2+2^{2018}\right)-1\)

\(\Rightarrow A=2^{2018}+2-1=2^{2018}+1\)   (2)

\(\left(1\right)\left(2\right)\Rightarrow S=\frac{2^{2018}+1}{1-2^{2018}}\)

làm đến đây thì............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................tớ ko bt lm nx