Question

Tính A=2/3+2/9+2/27+...+2/2187+2/6561 .Tính nhe mọi người, mình tick cho

Answer 1

\(A=\frac{2}{3}+\frac{2}{9}+\frac{2}{27}+...+\frac{2}{2187}+\frac{2}{6561}\)

\(3\times A=2+\frac{2}{3}+\frac{2}{9}+...+\frac{2}{729}+\frac{2}{2187}\)

\(3\times A-A=\left(2+\frac{2}{3}+\frac{2}{9}+...+\frac{2}{2187}\right)-\left(\frac{2}{3}+\frac{2}{9}+\frac{2}{27}+...+\frac{2}{2187}+\frac{2}{6561}\right)\)

\(2\times A=2-\frac{2}{6561}\)

\(A=\frac{6560}{6561}\)