= 0,7497362034

0,7497362034

Đặt \(A=\frac12+\frac16+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\frac{1}{486}+\frac{1}{1458}\)

\(=\frac12\left(1+\frac13+\frac19+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)\)

Đặt \(B=1+\frac13+\frac19+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

=>\(3\times B=3+1+\frac13+\frac19+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

=>\(3\times B-B=3+1+\frac13+\frac19+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}-1-\frac13-\frac19-\cdots-\frac{1}{729}\)

=>\(2\times B=3-\frac{1}{729}=\frac{2186}{729}\)

=>\(B=\frac{1093}{729}\)

=>\(A=\frac12\times\frac{1093}{729}=\frac{1093}{1458}\)

bài 5 ta tính tổng cả ba số đi rồi quy đồng tử số là ra có gì đâu

tính nhanh: 1/2+1/6+1/18+1/54+...1/486

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\frac{1}{486}\)

\(3\times A=\frac{3}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\)

\(3\times A-A=\left(\frac{3}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\right)-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\frac{1}{486}\right)\)

\(2\times A=\frac{3}{2}-\frac{1}{486}\)

\(A=\frac{182}{243}\)

182/243

3,748285322

374828532236

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