Question

Bạn nào giỏi toán giúp mk với:

Tính tống=3+3/2+3/2²+........+3/2( mũ 9)

Ai làm nhanh mk tick cho

Answer 1

\(A=3+\dfrac{3}{2}+\dfrac{3}{2^2}+....+\dfrac{3}{2^9}\)

\(2A=2\left(3+\dfrac{3}{2}+\dfrac{3}{2^2}+....+\dfrac{3}{2^9}\right)\)

\(2A=6+3+\dfrac{3}{2}+...+\dfrac{3}{2^8}\)

\(2A-A=\left(6+3+\dfrac{3}{2}+...+\dfrac{3}{2^8}\right)-\left(3+\dfrac{3}{2}+...+\dfrac{3}{2^9}\right)\)

\(A=6-\dfrac{3}{2^9}\)

Answer 2

Đặt A=3+3/2+3/2^2+...+3/2^9

A=3.(1/2+1/2^2+...+1/2^9)

Đặt B=1/2+1/2^2+...+1/2^9

=>B.2=1+1/2+1/2^2+...+1/2^8

=>2B-B=(1+1/2+...+1/2^8)-(1/2+1/2^2+...+1/2^9)

=>B=1-1/2^9

=>B=512/512-1/512

=>B=511/512

=>A=3.511/512

=>A=1533/512

Vậy A=1533/512

Answer 3

S=3+1/2.(3+3/2+3/2^2+...+3/2^8)

Mà 3+3/2+3/2^2+...+3/2^8=S-3/2^9

=>S=3+1/2.(S-3/2^9)

=>2S=6+S-3/3^9

=>S=6-3/2^9

=>S=6-3/512

>S=3069/512