Gọi biểu thức trên là A. Ta có
\(A=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)....\left(1-\dfrac{1}{2017}\right)\)
\(A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}....\dfrac{2016}{2017}=\dfrac{1.2.3...2016}{2.3.4..2017}=\dfrac{1}{2017}\)
\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{2017}-1\right)\)
Giải típ hộ mik nha !
\(\dfrac{1}{2}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{n.\left(n+1\right)}=\dfrac{2016}{2017}=\dfrac{1}{2.3}=\dfrac{1}{2}-\dfrac{1}{n+1}=\dfrac{2016}{2017}=\dfrac{n+1-2}{2.\left(n+1\right)}=\dfrac{2016}{2017}=\dfrac{n-1}{2.\left(n+1\right)}=\dfrac{2016}{2017}=2017.\left(n-1\right)=2016.2\left(n+1\right)=...\)
Tính:
a, \(\left(\dfrac{1}{2}+1\right).\left(\dfrac{1}{3}+1\right).\left(\dfrac{1}{4}+1\right)...\left(\dfrac{1}{99}+1\right)\)
b, \(\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right).\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{100}-1\right)\)
c, \(C=\dfrac{4}{30}+\dfrac{4}{70}+\dfrac{4}{126}+...+\dfrac{4}{798}\)
\(A=\left(1-\dfrac{1}{2}\right)\cdot1-\dfrac{1}{3}\cdot......\cdot\left(1-\dfrac{1}{2016}\right)\cdot\left(1-\dfrac{1}{2017}\right)\)
BT2: Tính nhanh
7) \(\left(-\dfrac{1}{2}\right)-\left(-\dfrac{3}{5}\right)+\left(-\dfrac{1}{9}\right)+\dfrac{1}{71}-\left(-\dfrac{2}{7}\right)+\dfrac{4}{35}-\dfrac{7}{18}\)
8)\(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)
Tính:
\(\left(\dfrac{1}{2}-1\right):\left(\dfrac{1}{3}-1\right):\left(\dfrac{1}{4}-1\right):\) ... : \(\left(\dfrac{1}{50}-1\right)\)
Chứng minh rằng:
\(\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{50}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+...+\dfrac{1}{100}+\dfrac{1}{102}\right)=\dfrac{1}{52}+\dfrac{1}{53}+...+\dfrac{1}{100}+\dfrac{1}{101}+\dfrac{1}{102}\)
2.Tính:
A=\(\left(\dfrac{1}{10}-1\right).\left(\dfrac{1}{11}-1\right)\left(\dfrac{1}{12}-1\right).....\left(\dfrac{1}{100}-1\right)\)
B=\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{10^2}\right)\)
C=\(\left(\dfrac{7}{9}+1\right)\left(\dfrac{7}{20}+1\right)\left(\dfrac{7}{33}+1\right)...\left(\dfrac{7}{108080}+1\right)\)
D=\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
tìm x biết
\(\left(3\dfrac{1}{2}+2x\right).2\dfrac{2}{3}=5\dfrac{1}{3}\)
\(\dfrac{3}{4}-2.\left|2x-\dfrac{2}{3}\right|=2\)
\(\left(0.6-\dfrac{1}{2}\right).\dfrac{3}{4}-\left(-1\right)=\dfrac{1}{3}\)
\(\left(3x-1\right).\left(-\dfrac{1}{2}x+5\right)=0\)
\(\dfrac{1}{4}+\dfrac{1}{3}:\left(2x-1\right)=-5\)
\(\left(2x+\dfrac{3}{5}\right)^2-\dfrac{9}{25}=0\)
\(-5.\left(x+\dfrac{1}{5}\right)-\dfrac{1}{2}.\left(x-\dfrac{2}{3}\right)=\dfrac{3}{2}x-\dfrac{5}{6}\)
Ruat gọn biểu thức:
T=\(\left(\dfrac{1}{2}+1\right).\left(\dfrac{1}{3}+1\right).\left(\dfrac{1}{4}+1\right).....\left(\dfrac{1}{98}+1\right).\left(\dfrac{1}{99}+1\right)\)