Question

Tính 

S= 1/2²+1/2³+1/2⁵+...+1/2¹⁰⁰

 

Answer 1

S=1/2²+1/2³+1/2⁴+...+1/2¹⁰⁰

=>2S=1/2+1/2²+1/2³+...+1/2⁹⁹

=>2S-S=(1/2+1/2²+1/2³+...+1/2⁹⁹)-(1/2+1/2²+1/2³+...+1/2⁹⁹)

=> S=1/2-1/2¹⁰⁰

Answer 2

\(2S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}\)

\(2S-S=S=\frac{1}{2}-\frac{1}{2^{100}}\)