Question

tính nhanh tổng sau:B= 1/9 + 1/9 + 1/81 + 1/729 +...+ 1 3^ 2008

help me please!:((

Answer 1

Lời giải:
\(P=\frac{1}{9}+\frac{1}{3^2}+\frac{1}{3^4}+\frac{1}{3^6}+...+\frac{1}{3^{2008}}\)

\(3^2P=1+1+\frac{1}{3^2}+\frac{1}{3^4}+...+\frac{1}{3^{2006}}\)

\(3^2P-P=(1+1+\frac{1}{3^2}+\frac{1}{3^4}+...+\frac{1}{3^{2006}})-(\frac{1}{9}+\frac{1}{3^2}+\frac{1}{3^4}+...+\frac{1}{3^{2008}})\)

\(8P=2-\frac{1}{9}-\frac{1}{3^{2008}}=\frac{17}{9}-\frac{1}{3^{2008}}\)

\(P=\frac{17}{72}-\frac{1}{8.3^{2008}}\)