Question

tính nhanh

B = (x:1-x.1).(x.2015+x+1).(x là số tự nhiên)

F = 2/6+2/12+....+2/240

G = 1/3+1/9+1/27+1/81+1/243

H = 1/2+1/4+1/8+...+1/1024

Answer 1

b: \(F=2\left(\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{240}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)

\(=2\cdot\dfrac{7}{16}=\dfrac{7}{8}\)

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

\(\Leftrightarrow2G=1-\dfrac{1}{243}=\dfrac{242}{243}\)

hay G=121/243

d: \(2H=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\)

\(\Leftrightarrow H=1-\dfrac{1}{1024}\)