Question

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

Answer 1

ko chép đề

2A=\(2+\frac{3}{2^2}+\frac{4}{2^3}+\frac{5}{2.5^5}+...+\frac{100}{2^{99}}\)    

đến đây mik thấy đề sai

đáng lẽ \(\frac{5}{5^5}\)phải là \(\frac{5}{2^5}\)

Answer 2

à đề sai đó, bn làm giúp mk vs
 

Answer 3

ok vậy bạn tham khảo link này :

https://olm.vn/hoi-dap/detail/16281729260.html

chịu khso gõ lên google nha

:)

Answer 4

bn làm giúp mk đi

Answer 5

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

\(\frac{1}{2}A=\frac{1}{2}+\frac{3}{2^4}+\frac{4}{2^5}+\frac{99}{2^{100}}+\frac{100}{2^{101}}\)

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

\(=\frac{\left[1-\left(\frac{1}{2}\right)^{101}\right]}{\left(1-\frac{1}{2}\right)-\frac{100}{2^{101}}}\)

\(=\frac{\left(2^{101}-1\right)}{2^{100}-\frac{100}{2^{101}}}\)

\(=\frac{\left(2^{101}-1\right)}{2^{99}-\frac{100}{2^{100}}}\)