a, = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9
= 1 - 1/9
= 8/9
b và c biến tử = hiệu giữa 2 thừa số ở mẫu rồi làm như a
A) \(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\)
\(=\frac{1}{1}-\frac{1}{9}\)
\(=\frac{8}{9}\)
B) \(=\frac{1}{4}\times\left(\frac{4}{5\times9}+\frac{4}{9\times13}+...+\frac{4}{129x133}\right)\)
\(=\frac{1}{4}\times\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{129}-\frac{1}{133}\right)\)
\(=\frac{1}{4}\times\left(\frac{1}{5}-\frac{1}{133}\right)\)
\(=\frac{1}{4}\times\frac{128}{665}\)
\(=\frac{32}{665}\)
C) \(=\frac{3}{4}\times\left(\frac{4}{7\times11}+\frac{4}{11x15}+...+\frac{4}{125x129}\right)\)
\(=\frac{3}{4}x\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{125}-\frac{1}{129}\right)\)
\(=\frac{3}{4}\times\frac{122}{903}\)
\(=\frac{61}{602}\)
TK nha ( mk k ghi lại đầu bài đâu lâu lắm ) !! :))
a) \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\)
\(=1-\frac{1}{9}\)
\(=\frac{8}{9}\)
b) \(\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{129.133}\)
\(=\frac{1}{4}.\left(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{129.133}\right)\)
\(=\frac{1}{4}.\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{129}-\frac{1}{133}\right)\)
\(=\frac{1}{4}.\left(\frac{1}{5}-\frac{1}{133}\right)\)
\(=\frac{1}{4}.\frac{128}{665}\)
\(=\frac{32}{665}\)
c) \(\frac{3}{7.11}+\frac{3}{11.15}+\frac{3}{15.19}+...+\frac{3}{125.129}\)
\(=\frac{3}{4}.\left(\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}+...+\frac{4}{125.129}\right)\)
\(=\frac{3}{4}.\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+...+\frac{1}{125}-\frac{1}{129}\right)\)
\(=\frac{3}{4}.\left(\frac{1}{7}-\frac{1}{129}\right)\)
\(=\frac{3}{4}.\frac{122}{903}\)
\(=\frac{61}{602}\)
_Chúc bạn học tốt_
a, 1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+...+1/8x9
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/8-1/9
=1/1-1/9
=1-1/9
=8/9
