cho mình hỏi câu này :
( 2x4+4x6+6x8+...+48x50) : (1x2+2x3+...+24x25)
( 8+16+24+...+800) : (4+8+12+...+400)
S=2x4+4x6+6x8+...+46x48+48x50
câu này cũngtính 6S à?
S = 2*4+4*6+6*8+...+46*48+48*50
S6 = 2*4*6+4*6*6+6*8*6+........................+46*48*6+48*50*6
S6=2*4*(6-0)+4*6*(8-2)+6*8*(10-4)+.................................+46*48*(50-44)+48*50*(52-46)
S6 = 2*4*6+4*6*8-2*4*6+6*8*10-4*6*8+..........................................+46*48*50-44*46*48+48*50*52-46*48*50
S6 = 48*50*52=124800
S=124800/6=20800
\(S=2\cdot4+4\cdot6+...+48\cdot50\)
\(S=2\left(1\cdot2+2\cdot3+...+24\cdot25\right)\)
\(\Rightarrow3S=2\left(1\cdot2\left(3-0\right)+2\cdot3\left(4-1\right)+...+24\cdot25\left(26-23\right)\right)\)
\(\Rightarrow3S=2\left(1\cdot2\cdot3-0\cdot1\cdot2+2\cdot3\cdot4-1\cdot2\cdot3+...+24\cdot25\cdot26-23\cdot24\cdot25\right)\)
\(\Rightarrow3S=2\cdot24\cdot25\cdot26\)
\(\Rightarrow S=2\cdot8\cdot25\cdot26=10400\)
\(\Rightarrow6S=10400\cdot6=62400\)
2x4+4x8+8x12+12x16+16x20
1x2+2x4+4x6+6x8+8x10
tính nhanh
Tính :
N = ( 1/2x4 + 1/4x6 + 1/6x8 + 1/8x10 + ....... + 1/98 X 100 ) : ( 1/2 + 1/4 + 1/8 + 1/16 + ........ + 1/512 )
b1 : tìm x
a] [ 1/2x5 + 1/5x8 + 1/8x11 + ......+ 1/65x68 ] x X = 11/68
b] X - [ 12/2x4 + 12/4x6 + 12/ 6x8+...+12/48x50 ] = 1/5
c] X + [ 5/5 + 5/45 + 5/117+ 5/221 + ...+5/1845 ] =2
1/1x2+1/2x3+1/3x4+1/24x25
1/1x2+ 1/2x3+1/3x4+1/24x25
\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+....+\dfrac{1}{24\times25}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{24}-\dfrac{1}{25}\)
\(=1-\dfrac{1}{25}\)
\(=\dfrac{24}{25}\)
So sánh:
A=\(\dfrac{1}{1x2}\)+\(\dfrac{1}{2x3}\)+.....+\(\dfrac{1}{49x50}\) với 1
B=\(\dfrac{1}{2x4}\)+\(\dfrac{1}{4x6}\)+.....+\(\dfrac{1}{46x48}\) với \(\dfrac{1}{4}\)
C=\(\dfrac{1}{6}\)+\(\dfrac{1}{12}\)+.....+\(\dfrac{1}{110}\)+\(\dfrac{1}{122}\) với \(\dfrac{1}{2}\)
Giải tất cả các câu đầy đủ phép tính giúp mik nha. C.ơn
\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{49\cdot50}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\)
\(=\dfrac{49}{50}< 1\)
tính A=1x3+2x4+3x5+4x6+...+48x50+49x51
các bạn giúp mình với!
4/ 2x4 +4/4x6+4/6x8+.......+4/2008x2010
\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)=\frac{2.2004}{2010}=\frac{2004}{1005}\)
\(=\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+...+\frac{2}{1004\cdot1005}\)
\(=2\cdot\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{1004\cdot1005}\right)\)
\(=2\cdot\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1004}-\frac{1}{1005}\right)\)
\(=2\cdot\left(1-\frac{1}{1005}\right)=2\cdot\frac{1004}{1005}=\frac{2008}{1005}\)
Cho B = 4\2x4 + 4\4x6 + 4\6x8 + ..... 4\98x100
Tính 5B ?
\(B=\dfrac{4}{2.4}+\dfrac{4}{4.6}+...+\dfrac{4}{98.100}\)
\(\Rightarrow5B=\dfrac{20}{2.4}+\dfrac{20}{4.6}+...+\dfrac{20}{98.100}\)
\(\Rightarrow5B=10\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{98.100}\right)\)
\(\Rightarrow5B=10\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)\)
\(\Rightarrow5B=10\left(\dfrac{1}{2}-\dfrac{1}{100}\right)\)
\(\Rightarrow5B=10.\dfrac{49}{100}\)
\(\Rightarrow5B=\dfrac{49}{10}\)
Vậy \(5B=\dfrac{49}{10}\)
Ta có: B = \(\dfrac{4}{2.4}\) + \(\dfrac{4}{4.6}\) + \(\dfrac{4}{6.8}\) + ... + \(\dfrac{4}{98.100}\).
=> \(\dfrac{B}{2}\) = \(\dfrac{2}{2.4}\) + \(\dfrac{2}{4.6}\) + \(\dfrac{2}{6.8}\) + ... + \(\dfrac{2}{98.100}\)
=\(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{8}\) + ... + \(\dfrac{1}{98}\) - \(\dfrac{1}{100}\)
= \(\dfrac{1}{2}\) - \(\dfrac{1}{100}\) = \(\dfrac{49}{100}\).
=> B = \(\dfrac{49}{200}\).
=> 5B = \(\dfrac{49}{200}\) . 5 = \(\dfrac{49}{40}\).
Vậy 5B = \(\dfrac{49}{40}\).