Question

[Đỗ Lê Minh Anh]

cac ban giup minh nhe:

1+2+2^2+...+2^2008/1-2^2008

cam on cac ban da giup minh

Answer 1

[Edogawa Conan]

\(\frac{1+2+2^2+...+2^{2008}}{1-2^{2008}}\)

Ta có: Đặt A = 1 + 2 + 2² + ... + 2²⁰⁰⁸

2A = 2 + 2² + 2³ + ... + 2²⁰⁰⁹

2A - A = (2 + 2² + 2³ + ... + 2²⁰⁰⁹) - (1 + 2 + 2² + ... + 2²⁰⁰⁸)

A = 2²⁰⁰⁹ - 1

=> \(\frac{1+2+2^2+...+2^{2008}}{1-2^{2008}}=\frac{2^{2009}-1}{1-2^{2008}}\)