Question

Tính nhanh tổng sau :

\(B=1+\frac{9}{45}+\frac{9}{105}+\frac{9}{189}+...+\frac{9}{29997}\)

Answer 1

=335510

Answer 2

335510

Answer 3

\(B=1+\frac{3}{5}+\frac{3}{35}+\frac{3}{55}+.....+\frac{3}{9999}\)

\(B=\frac{3}{1}.3+\frac{3}{3}.5+\frac{3}{5}.7+......+\frac{3}{99}.101\)

\(B=\frac{3}{2}\left(\frac{2}{1}.3+\frac{2}{3}.5+.......+\frac{3}{99}.101\right)\)

\(B=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.........+\frac{1}{99}-\frac{1}{101}\right)\)

\(B=\frac{3}{2}\left(1-\frac{1}{101}\right)\)

\(B=\frac{3}{2}.\frac{100}{101}\)

\(B=\frac{150}{101}\)