Question

Bai tap:tinh bang cach thuan tien nhat:

a 1/3+2/3+...+10/3+11/3=

b 9+9/2+9/4+9/8+...+9/128+9/256=

c) 5/3+5/3.5+5/5.7+...+5/101.103=

Answer 1

a) = \(\frac{1+2+3+..+11}{3}=\frac{\left(1+11\right)+\left(2+9\right)+..+\left(5+7\right)+6}{3}=\frac{12.5+6}{3}=\frac{66}{3}=22\)

Answer 2

b)          A = \(9+\frac{9}{2}+\frac{9}{4}+\frac{9}{8}+...+\frac{9}{128}+\frac{9}{256}\)

2 x A = 18 + 9 + \(\frac{9}{2}+\frac{9}{4}+\frac{9}{8}+...+\frac{9}{128}\)

Lấy 2 x A - A = 18 - \(\frac{9}{256}\)

A = 4599/256

Answer 3

c) \(B=\frac{5}{1\times3}+\frac{5}{3\times5}+\frac{5}{5\times7}+...+\frac{5}{101\times103}\)

\(B=\frac{5}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{25}{101\times103}\right)\)

\(B=\frac{5}{2}\times\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{101}-\frac{1}{103}\right)=\frac{5}{2}\times\left(1-\frac{1}{103}\right)\)= 255/103