Question

cho S=2+2^2+2^3+...+2^100.Tính tổng 

 

Answer 1

Ta có: S=2+2²+2³+......+2¹⁰⁰          (1)

=> 2S=2²+2³+2⁴+.........+2¹⁰¹     (2)

lấy (2)-(1) ta có:

2S-S=(2²+2³+2⁴+...........+2¹⁰¹)-(2+2²+2³+........+2¹⁰⁰)

=> S=2¹⁰¹-2

Answer 2

\(S=2+2^2+2^3+...+2^{100}\)

\(\Rightarrow2S=2+2^2+...+2^{99}\)

\(\Rightarrow2S-S=\left(2+2^2+...+2^{99}\right)-\left(2+2^2+2^3+...+2^{100}\right)\)

\(\Rightarrow\left(2-1\right).S=\left(2+2^2+...+2^{99}\right)-\left(2+2^2+2^3+...+2^{100}\right)\)

\(\Rightarrow S=1-2^{100}\Leftrightarrow S=...\)