Question

A = 1+1/2+1/2²+1/2³+...+1/2²⁰¹⁶

^{(Mình cần gấp)}

Answer 1

\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\)

\(2A-A=2+1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2015}}-1-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{2016}}\)

Liệt những số đối nhau:

\(A=2-\frac{1}{2^{2016}}\)

\(A=\frac{2^{2017}-1}{2^{2016}}\)

Chúc em học tốt^^

Answer 2

bạn nhân cả 2 vế với 2 rồi lấy 2A-A là ra kq

k mik nhé

Answer 3

B = 1/2+(1/2)²+(1/2)³+...+ (1/2)⁹⁸+(1/2)⁹⁹+(1/2)⁹⁹

 => 1/2B = (1/2)²+(1/2)³+...+ (1/2)⁹⁸+(1/2)⁹⁹+(1/2)¹⁰⁰+(1/2)¹⁰⁰

 1/2B- B = [(1/2)²+(1/2)³+...+ (1/2)⁹⁸+(1/2)⁹⁹+(1/2)¹⁰⁰+(1/2)100] - [ 1/2+(1/2)²+(1/2)³+...+ (1/2)⁹⁸+(1/2)⁹⁹+(1/2)⁹⁹]

     -1/2B = [(1-2)²-(1/2)²]+[(1/2)³-(1/2)³]+...+[(1/2)⁹⁸-(1/2)⁹⁸]+[(1/2)⁹⁹-(1/2)⁹⁹]+[(1/2)¹⁰⁰+(1/2)¹⁰⁰-(1/2)⁹⁹] -1/2

     -1/2B = 0+0+...+0+0+0-1/2

     -1/2B = -1/2

=>       B = 1 mik tính tới (1/2)^{99 thôi}