Question

Nữa nè ;))

Answer 1

\(S=1+\dfrac{3}{2^3}+\dfrac{4}{2^4}+\dfrac{5}{2^5}+...+\dfrac{100}{2^{100}}\)

\(2S=2\left(1+\dfrac{3}{2^3}+\dfrac{4}{2^4}+\dfrac{5}{2^5}+...+\dfrac{100}{2^{100}}\right)\)

\(2S=2+\dfrac{3}{2^2}+\dfrac{4}{2^3}+\dfrac{5}{2^4}+...+\dfrac{100}{2^{99}}\)

\(2S-S=\left(2+\dfrac{3}{2^2}+...+\dfrac{100}{2^{99}}\right)-\left(1+\dfrac{3}{2^3}+...+\dfrac{100}{2^{100}}\right)\)

\(S=\left(2-1\right)+\dfrac{3}{2^2}+\left(\dfrac{1}{2^3}+\dfrac{1}{2^4}...+\dfrac{1}{2^{99}}\right)-\dfrac{100}{2^{100}}\)

\(S=1+\dfrac{3}{2^2}-\dfrac{100}{2^{100}}+\dfrac{1}{2^2}-\dfrac{1}{2^{99}}=2-\dfrac{100}{2^{100}}-\dfrac{1}{2^{99}}\)

Answer 2

50