Truy cập link để nhận thẻ cào 50k free :

http://123link.vip/7K2YSHxh

Nhanh không cả hết !

\(A=1+\frac{3}{2^3}+\frac{4}{2^4}+\frac{5}{2^5}+...+\frac{100}{2^{100}}\)

\(\Rightarrow2A=2+\frac{3}{2^2}+\frac{4}{2^3}+...+\frac{100}{2^{99}}\)

\(\Rightarrow A=1+\frac{3}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}}-\frac{100}{2^{100}}\)

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

    \(\Rightarrow2B=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{98}}\)

\(\Rightarrow B=2-\frac{1}{2^{99}}\Rightarrow A=2-\frac{1}{2^{99}}-\frac{100}{2^{100}}\)

sao từ nãy đến giờ sao cứ thế toán lớp 7 không có toán lớp 4

\(\frac{1}{2}A=\frac{1}{2}+\frac{3}{2^4}+\frac{4}{2^5}+...+\frac{100}{2^{101}}.\)

\(A-\frac{1}{2}A=\frac{1}{2}+\frac{3}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+...+\frac{1}{2^{100}}-\frac{1}{2^{101}}\)

\(\frac{1}{2}A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{100}}-\frac{1}{2^{101}}\)(TA PHÂN TÍCH 3/2^3=1/2^2+1/2^3)

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

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

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

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

\(\Rightarrow\frac{1}{2}A=1-\frac{1}{2^{100}}-\frac{1}{2^{101}}\)

\(\Leftrightarrow A=2-\frac{1}{2^{99}}-\frac{1}{2^{100}}=\frac{2^{101}-3}{2^{100}}\)

học tốt....