A ) a = 1/2 + 1/6 + 1/18 + 1/54 + 1/162
B ) 1/2 + 1/6 + 1/ 12 + 1/ 20 + ...+ 1/ 9900
C ) 20.2*5.1-30.3*3.4+14.56/ 14.58*460+7.29 *540*2
* đây là dấu nhân nhé
Tính nhanh
A ) 20.2 × 5.1 - 30.3 × 3.4 +14.58
14.58 × 460 + 7.29 × 540 × 2
Biến đổi tử số và mẫu số,ta có :
Tử số : 20,2 x 51 - 30,3 x 3,4 + 14,58
= 103,02 - 103,02 + 14.58
= 0 + 14,58 = 14,58
Mẫu số : 14,58 x 460 + 7,29 x 540 x 2
= 14,58 x 460 + 14,58 x 540
= 14,58 x \((460+540)\)
= 14.58 x 1000
= 14580
Thay vào ta có : = 14,58 : 14580
= 0,001
Vậy : \(\frac{20,2\cdot5,1-30,3\cdot3,4+14,58}{14,58\cdot460+7,29\cdot540\cdot2}=0,001\)
~Chúc bn học giỏi~
tính nhanh :
Cho phân số
20.2 x 5.1 - 30.3 x 3.4 + 14.88
14.58 x 460 + 7.29 x 540 x 2
20,2*5.1-30.3*3.4+14.58
14.58*460+7.29*540*2
20,2*5,1-30,3*3,4+14,58
=103,02-103,02+14,58
=14,58
14,58*460+7,92*540*2
=6706,8+4276,8*2
=6706,8+8553,6
=15260,4
A=1/1.2+1/2.3+1/3.4+1/4.5+...+1/98.99+1/99.100
B=2/1.3+2/3.5+2/5.7+2/7.9+...+2/97.99+2/99.101
C=1/2+1/4+1/8+1/16+...+1/1024+1/2048
D=1/2+1/6+1/18+1/54+1/4374+1/13122 ( . (DẤU CHẤM LÀ ''NHÂN'')
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}=\frac{99}{100}\)
\(B=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}+\frac{2}{99.101}\)
\(=1-\frac{1}{3}+\frac{!}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(=1-\frac{1}{101}=\frac{100}{101}\)
\(C=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{1024}+\frac{1}{2048}\)
\(\Rightarrow\)\(2C=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{512}+\frac{1}{1024}\)
\(\Rightarrow\)\(2C-C=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\right)\)
\(\Leftrightarrow\)\(C=1-\frac{1}{2048}=\frac{2047}{2048}\)
Câu A bạn quên 1/4.5 kìa , với câu D đâu >>>
Tìm x (nhanh):
a, 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + x = 3/5
b, 2/3.5 + 2/5.7 + ... + 2/13.15 + x = 1/3
c, 1/2 + 1/6 + 1/12 + 1/20 + ... + 1/x( x + 1) = 9/10
Ở cậu b dấu chấm là dấu nhân đấy nhé!!!
Giải ra nhé!!!
a)\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{2}{5}+x=\frac{3}{5}\)
\(\Rightarrow x=\frac{3}{5}-\frac{2}{5}=\frac{1}{5}\)
b)\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...+\frac{2}{13}-\frac{2}{15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}-\frac{2}{15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{8}{15}+x=\frac{1}{3}\)
\(\Rightarrow x=\frac{1}{3}-\frac{8}{15}=-\frac{1}{5}\)
c)\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Leftrightarrow\frac{x+1-1}{x+1}=\frac{9}{10}\)
\(\Rightarrow\frac{x}{x+1}=\frac{9}{10}\)
\(\Rightarrow x=9\)
b) \(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{15-13}{13.15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{15}+x=\frac{1}{3}\)
\(\Leftrightarrow x=\frac{1}{15}\)
1/2 + 1/6 + 1/12 + 1/20 + 1/30
câu2 : 20,2 x 3 x 1,7 - 30,3 x 2 x 1,7 + 14, 58 /14,58 x 460 + 7,29 x 540 x 7
1.Ta có:1/2=1/1.2
1/6=1/2.3
1/12=1/3.4
........
=>1/2+1/6+1/12+1/20+1/30=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6
2.hinh nhu sai đe
D=1/2+1/6+1/18+1/54+1/4374+1/13122 ( . (DẤU CHẤM LÀ ''NHÂN'')
A)17/5.-31/125.1/2.10/17.-1/2 mũ 3
B)(11/4.-5/9.4/9.11/4).8/33
C)(135/21 +45/123 - 55/434).(-5/12 + 1/4 + 1/6
D) 132/111. (1 /2 + 1/3 + 7/6)
E)1/5.1/6 + 1/6.1/7 + 1/7.1/8 + 1/8 . 1/9 + 1/9.9/10
F)1/90 + 1/110 + 1/132 +1/156+1/182
Mấy cái dấu / này là dấu phân số nha.Còn dấu chấm là
dấu nhân
Bài1:Tính giá trị của biểu thức
a.2/5.1/3-2/15:1/5+3/5.1/3
b.[6+(1/2)3- l-1/2l]:3/12
c.(-1/2)2:1/4-2(-1/2)2
d.F=4/2.4+4/4.6+4/6.8+...+4/2008.2010
e.F=1/18+1/54+1/108+...+1/990
a: \(=\dfrac{2}{15}-\dfrac{2}{15}\cdot5+\dfrac{3}{15}=\dfrac{2-10+3}{15}=\dfrac{-5}{15}=\dfrac{-1}{3}\)
b: \(=\left(6+\dfrac{1}{8}-\dfrac{1}{2}\right)\cdot4=\dfrac{48+1-4}{8}\cdot4=\dfrac{45}{2}\)
c: \(=\dfrac{1}{4}\cdot4-2\cdot\dfrac{1}{4}=1-\dfrac{1}{2}=\dfrac{1}{2}\)
d: \(F=2\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{2008\cdot2010}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)
\(=2\cdot\dfrac{1004}{2010}=\dfrac{1004}{1005}\)