Question

[Hồ Trâm Anh]

 Tính( rút gọn)

 C=1+1/2+1/2²+1/2³+...+1/2¹⁰⁰

 ^{tinh giup minh nha}

Answer 1

[van anh ta]

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

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

                         \(2C-C=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+2^{99}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\right)\)

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

                   Ủng hộ mk nha bn !!! ^_^

Answer 2

[Nguyễn Thị Hương Giang]

2C= 2+1+1/2+1/2²+.....+1/2⁹⁹

2C-C= ( 2+1+1/2+1/2²+.....+1/2⁹⁹ ) - (1+1/2+1/2²+1/2³+.....+1/2¹⁰⁰)

C= 2 - 1/2¹⁰⁰

C=2