Question

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1000}{3^{100}}\)

Chững minh a<\(\frac{3}{4}\)

Answer 1

\(A=\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{100}}\)

\(3A=1+\frac{1}{3}+...+\frac{1}{3^{99}}\)

\(2A=1-\frac{1}{3^{100}}\)

\(A=\frac{1-\frac{1}{3^{100}}}{2}< \frac{1-\frac{1}{3}}{2}=\frac{\frac{2}{3}}{2}=\frac{2}{3}.\frac{1}{2}=\frac{1}{3}< \frac{3}{4}\)

Answer 2

vậy \(\frac{1}{^{3^{100}}}\) đâu bạn

mình ko hiểu tại sao lai còn \(\frac{1}{3}\)