Question

tính

G= \(\dfrac{1}{2}\)+ \(\dfrac{1}{2^2}\)+\(\dfrac{1}{2^3}\)+...+\(\dfrac{1}{2^5}\)

Q=\(\dfrac{1}{2}\)+\(\dfrac{1}{2^2}\)+\(\dfrac{1}{2^3}\)+...+ \(\dfrac{1}{2^{10}}\)

m.n giúp e vs nhé\! trình bày rõ ràng nha^^ cảm ơn nhiều ạ <3

Answer 1

\(G=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}\)

\(\Rightarrow2G=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}\)

\(\Rightarrow2G-G=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}\right)\)

\(\Rightarrow G=1-\dfrac{1}{32}=\dfrac{31}{32}\)