b) Ta có: \(B=\dfrac{1}{10\cdot11}+\dfrac{1}{11\cdot12}+\dfrac{1}{12\cdot13}+\dfrac{1}{13\cdot14}\)
\(=\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{14}\)
\(=\dfrac{1}{10}-\dfrac{1}{14}\)
\(=\dfrac{14}{140}-\dfrac{10}{140}\)
\(=\dfrac{4}{140}=\dfrac{1}{35}\)
1/1.2 + 1/2.3 + 1/3.4 + ... + 1/99.100
1so sánh: \(\frac{1}{5}\)-\(\frac{1}{6}\) với\(\frac{1}{5.6}\)
\(\frac{1}{6}\) - \(\frac{1}{7}\)với \(\frac{1}{6.7}\)
2. Tính nhanh
\(\frac{1}{1.2}\)+ \(\frac{1}{2.3}\)+ \(\frac{1}{3.4}\)+\(\frac{1}{4.5}\) + \(\frac{1}{5.6}\)
Nhanh nhanh mai em nộp
Tính
S = 1/1.2+1/2.3+1/3.4+1/4.5
P= 1/1.3+1/3.5+1/5.7+1/7.9
a) Cho hai phân số \(\dfrac{1}{n}\) và \(\dfrac{1}{n+1},\left(n\in\mathbb{Z},n>0\right)\). Chứng tỏ rằng tích của hai phân số này bằng hiệu của chúng ?
b) Áp dụng kết quả trên để tính giá trị của các biểu thức sau :
\(A=\dfrac{1}{2}.\dfrac{1}{3}+\dfrac{1}{3}.\dfrac{1}{4}+\dfrac{1}{4}.\dfrac{1}{5}+\dfrac{1}{5}.\dfrac{1}{6}+\dfrac{1}{6}.\dfrac{1}{7}+\dfrac{1}{7}.\dfrac{1}{8}+\dfrac{1}{8}.\dfrac{1}{9}\)
\(B=\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\)
Tính một cách hợp lý:
a\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{100}-1\right)\)) \(x:\dfrac{99}{100}:\dfrac{98}{99}:...:\dfrac{2}{3}:\dfrac{1}{2}\)
b) \(\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}\)
c) \(\dfrac{\dfrac{1}{9}-\dfrac{5}{6}-4}{\dfrac{7}{12}-\dfrac{1}{36}-10}\)
d) \(\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)...\left(\dfrac{1}{99}+1\right)\)
e)
Tính các tích sau:
A=3/4 . 8/9 .15/16 . ..... . 9999/10000
B=(1 - 1/4)(1 - 1/9). ..... . (1 - 1/10000)
C=(1 + 1/1.3)(1 + 1/2.4)(1 + 1/3.15). ..... .(1 + 1/99.100)
Bài 1: \(\frac{1}{6}\)+\(\frac{-5}{7}\): x = \(\frac{-7}{18}\)
Bài 2: Tìm tích
a)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)...\left(\frac{1}{999}+1\right)\)
b)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{1000}-1\right)\)
c)\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{99}{10^2}\)
X/2018-1/70-1/15-1/21-...-1/120=5/8
(11/12+11/12.23+11/23.34+....+2/89.100)+x=5/3
(2'11.13+2/13.15+...+2/19.21)-x+4+221/231=7/3
Tìm x biết
a)\(\dfrac{11}{12}\).x + \(\dfrac{3}{4}\)= -\(\dfrac{1}{6}\)
b)3-\(\left(\dfrac{1}{6}-x\right)\).\(\dfrac{2}{3}\)=\(\dfrac{2}{3}\)
