Question

tính dãy tính sau

1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

Answer 1

\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(=\frac{729}{729}+\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\frac{3}{729}+\frac{1}{729}\)

\(=\frac{729+243+81+27+9+3+1}{729}\)

\(=\frac{1087}{729}\)

Answer 2

Đặt \(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(3A=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(3A-A=3-\frac{1}{729}\)nên \(2A=3-\frac{1}{729}\)

kHI ĐÓ \(A=\left(3-\frac{1}{729}\right):2=\frac{3}{2}-\frac{1}{1458}=\frac{2197}{1458}-\frac{1}{1458}=\frac{2196}{1458}\)

Answer 3

 \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\)\(\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(=\frac{729}{729}+\frac{243}{729}+\)\(\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\)\(\frac{3}{729}\)\(+\frac{1}{729}\)

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

Answer 4

1+\(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

=\(\frac{729}{729}\)+\(\frac{243}{729}\)+\(\frac{81}{729}\)+\(\frac{27}{729}\)+\(\frac{9}{729}\)+\(\frac{3}{729}\)+\(\frac{1}{729}\)

=\(\frac{729+243+81+27+9+3+1}{729}\)

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

Answer 5

\(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(=\frac{729}{729}+\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{9}{729}+\frac{3}{729}+\frac{1}{729}\)

\(=\frac{729+243+81+27+9+3+1}{729}=\frac{1093}{729}\)

Đáp số: \(\frac{1093}{729}\)