Question

1/3+1/3³+1/3⁵+1/3⁷+...+1/3⁹⁹+1/3¹⁰¹

Answer 1

Lời giải:

Đặt biểu thức là $A$

\(A=\frac{1}{3}+\frac{1}{3^3}+\frac{1}{3^5}+....+\frac{1}{3^{99}}+\frac{1}{3^{101}}\)

\(3^2.A=3+\frac{1}{3}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\)

Trừ theo vế:

\(8A=3-\frac{1}{3^{101}}\Rightarrow A=\frac{3}{8}-\frac{1}{8.3^{101}}\)