tính nhanh \(S=\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{1024}\)

tính nhanh \(S=\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{1024}\)

Tính nhanh :

F=\(\dfrac{2}{6}\)+\(\dfrac{2}{12}+...+\dfrac{2}{240}\)

G= \(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\)

H= \(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{1024}\)

\(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{1024}\)

Tính nhanh

A=\(\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{4}\right)+\left(1-\dfrac{1}{8}\right)+...+\left(1-\dfrac{1}{1024}\right)\)

B=4.5¹⁰⁰ .\(\left(\dfrac{1}{5}+\dfrac{1}{5^2}+\dfrac{1}{5^3}+...+\dfrac{1}{5^{100}}\right)+1\)

chứng minh rằng 

a , \(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+...+\dfrac{1}{512}-\dfrac{1}{1024}\) < \(\dfrac{1}{3}\)

b , \(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}\) < \(\dfrac{3}{16}\)

tính tổng S = \(\dfrac{1}{2}+\dfrac{2}{4}+\dfrac{3}{8}+\dfrac{4}{16}+...+\dfrac{10}{2^{10}}\)

làm nhanh hộ mình với

Câu 2 : Tính nhanh:

 \(\dfrac{1}{2}\)+\(\dfrac{1}{4}\)+\(\dfrac{1}{8}\)+...+\(\dfrac{1}{256}\)+\(\dfrac{1}{512}\)