Question

S=1+2+2 mũ 2+2 mũ 3+...+2 mũ 99+2 mũ 100 kèm giải thích ạ

Answer 1

`#3107`

`S = 1 + 2 + 2^2 + 2^3 + ... +`\(2^{99}+2^{100}\)

\(2S=2+2^2+2^3+2^4+...+2^{100}+2^{101}\)

`2S - S`

\(=\left(2+2^2+2^3+2^4+...+2^{100}+2^{101}\right)-\left(1+2+2^2+2^3+...+2^{99}+2^{100}\right)\)

\(S=2+2^2+2^3+2^4+...+2^{100}+2^{101}-1-2-2^2-2^3...-2^{99}-2^{100}\)

\(S=2^{101}-1\)

Vậy, \(S=2^{101}-1.\)

Answer 2

     S   = 1 + 2 + 2² + 2³ +...+ 2⁹⁹ + 2¹⁰⁰

   2S   =        2 + 2² + 2³ +...+ 2⁹⁹ + 2¹⁰⁰ + 2¹⁰¹

2S - S = 2¹⁰¹ - 1

        S = 2¹⁰¹ -1