1) A=7/10.11+7/10.12+7/10.13+...+7/69.70
2) B=1/25.27+1/27.29+1/29.31+...+1/73.75
3) C=4/2.4+4/4.6+4/6.8+...+4/2008.2010
Tính nhanh
1)A=\(\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
2)B=\(\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)
3)C=\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
A = \(\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
=\(7\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)
=\(7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)
=\(7\left(\frac{1}{10}-\frac{1}{70}\right)\)
=\(7.\frac{3}{35}\)
=\(\frac{3}{5}\)
B=\(\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)
=\(\frac{1}{2}\left(\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\right)\)
=\(\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
=\(\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\)
=\(\frac{1}{2}.\frac{2}{75}\)
=\(\frac{1}{75}\)
C : có ở bên dưới rồi, còn A và B thôi
1) A=7(\(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-......+\frac{1}{69}-\frac{1}{70}\) )
A=7 ( \(\frac{1}{10}-\frac{1}{70}\))
A=7x 6/70
A=3/5
tính:
1/25.27+1/27.29+1/29.31+...+1/73.75
4/2.4 + 4/4.6 +4/6.8 +...+ 4/2008.2010
a, \(\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}\)
\(=\frac{1}{2}\left(\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\right)\)
\(=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(=\frac{1}{2}\left(\frac{2}{75}\right)\)
\(=\frac{1}{75}\)
b, \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1004}{2010}\right)\)
\(=2\left(\frac{502}{1005}\right)\)
\(=\frac{1004}{1005}\)
Tk hộ =v
\(\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{75}\right)=\frac{1}{2}.\frac{2}{75}=\frac{1}{75}\)
\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)=2.\left(\frac{1}{2}-\frac{1}{2010}\right)=2.\frac{502}{1005}=\frac{1004}{1005}\)
\(\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)
\(=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(=\frac{1}{2}.\left(\frac{3}{75}-\frac{1}{75}\right)\)
\(=\frac{1}{2}.\frac{2}{75}\)
\(=\frac{1}{75}\)
Câu dưới đặt 2 ra ngoài rồi làm bình thường.
tính tổng
a, A=\(\frac{7}{10.11}\)+\(\frac{7}{11.12}\)+\(\frac{7}{12.13}\)+.......+\(\frac{7}{69.70}\)
b, B=\(\frac{1}{25.27}\)+\(\frac{1}{27.29}\)+\(\frac{1}{29.31}\)+.........+\(\frac{1}{73.75}\)
c, C=\(\frac{4}{2.4}\)+\(\frac{4}{4.6}\)+\(\frac{4}{6.8}\)+.............+\(\frac{4}{2008.2010}\)
a,
suy ra A = 7. (1/10.11+1/11.12+1/12.13+.......+1/69.70)
suy ra A = 7. ( 1/10 - 1/11+ 1/11 - 1/12 + 1/12 - 1/13+ ............. + 1/69 - 1/70)
suy ra A = 7. ( 1/ 10 - 1/70)
suy ra A= 7. 3/35
suy ra A= 3/5
A=\(\frac{1}{7}\)x(\(\frac{1}{10}\)+\(\frac{1}{11}\)+\(\frac{1}{11}\)+\(\frac{1}{12}\)+\(\frac{1}{12}\)+\(\frac{1}{13}\)+......+\(\frac{1}{69}\)+\(\frac{1}{70}\))
A=\(\frac{1}{7}\)x(\(\frac{1}{10}\)+\(\frac{1}{70}\))
A=\(\frac{1}{7}\)x(\(\frac{7}{70}\)+\(\frac{1}{70}\))
A=\(\frac{1}{7}\)x\(\frac{4}{35}\)
A=\(\frac{4}{245}\)
Tính các tổng sau
B= 1 / 25.27 + 1 / 27.29 + 1 / 29.31 + ....... + 1 / 73.75
C= 4 / 2.4 + 4 / 4.6 + 4 / 6.8 + ........+ 4 / 2008.2010
LÀM ƠN GIÚP MÌNH VỚI ĐƯỢC KO ..........HU HU
\(\text{Ta có:}\) \(C=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(\Rightarrow\frac{1}{2}C=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{2008.2010}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{2008}-\frac{1}{2010}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{2}-\frac{1}{2010}\)
\(\Rightarrow\frac{1}{2}C=\frac{502}{1005}\)
\(\Rightarrow C=\frac{502}{1005}:\frac{1}{2}=\frac{1004}{1005}\)
Ta có: \(B=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}\)
\(\Rightarrow2B=\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\)
\(\Rightarrow2B=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+....+\frac{1}{73}-\frac{1}{75}\)
\(\Rightarrow B=\left(\frac{1}{25}-\frac{1}{75}\right):2\)
\(\Rightarrow B=\frac{1}{75}\)
Vậy \(B=\frac{1}{75}\)
\(C=\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{2008.2010}\)
\(\Rightarrow\frac{2}{4}C=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\)
\(\Rightarrow\frac{2}{4}C=\frac{1}{2}-\frac{1}{2010}=\frac{502}{1005}\)
\(\Rightarrow C=\frac{502}{1005}:\frac{2}{4}=\frac{1004}{1005}\)
Vậy \(C=\frac{1004}{1005}\)
Ủng hộ tớ nha m.n ^_^
B = 1/25 - 1/27 + 1/27 - 1/29 + 1/29 - 1/31 +...+ 1/73 - 1/75
B = 1/25 - 1/75
B = 3/75 - 1/75 . B = 2/75
B=1/25.27+1/27.29+1/29.31+......+1/73.75
F=4/2.3+4/4.6+4/6.8+.....+4/2008.2010
Tính tổng đó nha các bạn
Ta có :
\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)
\(2B=\frac{2}{25.27}+\frac{1}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\)
\(2B=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+....+\frac{1}{73}-\frac{1}{75}\)
\(2B=\frac{1}{25}-\frac{1}{75}\)
\(2B=\frac{2}{75}\)
\(\Rightarrow B=\frac{1}{75}\)
Vậy B = \(\frac{1}{75}\)
\(F=\frac{4}{2.3}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(\Rightarrow F=2\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2008.2010}\right)\)
\(\Rightarrow F=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(\Rightarrow F=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(\Rightarrow F=2.\frac{502}{1005}=\frac{1004}{1005}\)
Vậy F = \(\frac{1004}{1005}\)
A=7/10.11+7/11.12+7/12.13+...+7/69.70
B=1/25.27+1/27.29+1/29.31+...+1/73.75
1) A = 7/ 10.11 + 7/ 11.12 + 7/ 12.13 + .... + 7/69.70
2 ) B = 1/ 25.27 + 1/ 27.29 + 1/29.31+ ......+ 1/ 73.75
1) A=7/10.11+7/11.12+7/12.13+...+7/69.70
A=7.(1/10.11+1/11.12+1/12.13+...+1/69.70)
A= 7.(1/10-1/11+1/11-1/12+1/12-1/13+...+1/69-1/70)
A= 7.(1/10-1/70)
A=7.3/35=3/5
2)B=1/25.27+1/27.29+1/29.31+...+1/73.1/75
B=1/25-1/27+1/27-1/29+1/29-1/31+...+1/73-1/75
B=1/25-1/75=2/75
A = 7/ 10.11 + 7/ 11.12 + 7/ 12.13 + .... + 7/69.70
(1/7).A=1/10.11+1/11.12+...+1/69.70
=1/10-1/11+1/11-1/12+...+1/69-1/70
=1/10-1/70=3/35
=>A=7.(3/35)
=3/5
2 ) B = 1/ 25.27 + 1/ 27.29 + 1/29.31+ ......+ 1/ 73.75
=>(1/2).B=2/25.27+...+2.73.75
=1/25-1/27+...+1/73-1/75
=1/25-1/75
=2/75
=>B=4/75
A=7.(1/10.11+1/11.12+1/12.13+...+1/69.70)
A= 7.(1/10-1/11+1/11-1/12+1/12-1/13+...+1/69-1/70)
A= 7.(1/10-1/70)
A=7.3/35=3/5
2)B=1/25.27+1/27.29+1/29.31+...+1/73.1/75
B=1/25-1/27+1/27-1/29+1/29-1/31+...+1/73-1/75
B=1/25-1/75=2/75
Bài 6: Tính các tổng sau:
A= \(\dfrac{7}{10.11}\)+\(\dfrac{7}{11.12}\)+\(\dfrac{7}{12.13}\)+...+\(\dfrac{7}{69.70}\)
B= \(\dfrac{1}{25.27}\)+\(\dfrac{1}{27.29}\)+\(\dfrac{1}{29.31}\)+...+\(\dfrac{1}{73.75}\)
\(A=7\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)
\(=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)=\dfrac{7.60}{700}=\dfrac{420}{700}=\dfrac{3}{5}\)
\(B=\dfrac{1}{2}\left(\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}-\dfrac{1}{29}+...+\dfrac{1}{73}-\dfrac{1}{75}\right)\)
\(=\dfrac{1}{2}\left(\dfrac{1}{25}-\dfrac{1}{75}\right)=\dfrac{1}{75}\)