Question

S =1+2+2mũ 2 + 2 mũ 3 +........2 mũ 100

Answer 1

\(S=1+2+2^2+2^3+...+2^{100}\)

\(2S=2+2^2+2^3+2^4+...+2^{101}\)

\(2S-S=\left(2+2^3+..+2^{101}\right)-\left(1+2^2+...+2^{100}\right)\)

\(S=2^{201}-1\)

Answer 2

Ta có 

S = 1 + 2 + 2² + 2³ + ....+ 2¹⁰⁰

2S = 2 + 2² + 2³ + 2^{4 + .} ....+ 2¹⁰¹

2S-S = ( 2 + 2² + 2³ + 2^{4 + .} ....+ 2¹⁰¹) - ( 1 + 2 + 2² + 2³ + ....+ 2¹⁰⁰)

S = 2 + 2² + 2³ + 2^{4 + .} ....+ 2¹⁰¹  - 1 -2 - 2²  - 2³ -....-  2¹⁰⁰

S = 2¹⁰¹ - 1