Kết quả là 63/128 dễ thế ko biết đg dùng máy tính ak
mẫu số chung cách éo hay,chú nhân 2 ên r lấy 2a-a là xong
Đặt A=1/4+1/8+1/16+1/32+1/64+1/128
2A=1/2+1/4+1/8+1/16+1/32+1/64
2A-A=1/2-1/128
A=64/128-1/128
A=63/128
Đặt \(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(\Rightarrow A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\)
\(\Rightarrow2A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\)
\(\Rightarrow2A-A=\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\right)\)
\(\Rightarrow A=\frac{1}{2^1}-\frac{1}{2^7}\)
\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(=\frac{1}{2.2}+\frac{1}{2.4}+\frac{1}{4.4}+\frac{1}{4.8}+\frac{1}{8.8}+\frac{1}{8.16}\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}\)
\(=\frac{1}{2}-\frac{1}{16}\)
\(=\frac{7}{16}\)
Hehehe:) Sai đó nha bạn!
tính nhanh p/s 1+ 5/4 + 5/8 + 5/16 + 5/32 + 5/64
