1/2+2/2x4+3/4x7+4/7x11+5/11x16
Tính nhanh
E = 1/1x2 + 2/2x4 + 3/4x7 + 4/7x11 + 5/11x16
\(E=\dfrac{1}{1\times2}+\dfrac{2}{2\times4}+\dfrac{3}{4\times7}+\dfrac{4}{7\times11}+\dfrac{5}{11\times16}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}\)
\(=1-\dfrac{1}{16}=\dfrac{15}{16}\)
#kễnh
A=1/1x2 + 2/2x4 + 3/4x7 + 4/7x11 + 5/11x16 + 6/16x22 + 7/22x29=....?
A=1/1-1/2+1/2-1/4+1/4-1/7+1/7-1/11+1/11-1/16+1/16-1/22+1/22-1/29
A=1/1-1/29
A=28/29
tính nhanh
a 1/2+2/2x4+3/4x7+4/7x11+5/11x16
b 3/54+4/117+5/234+6/432+7/744
1/1x2+2/2x4+3/4x7+4/7x11+...+11/56x67
\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{56}-\dfrac{1}{67}\)
\(=1-\dfrac{1}{67}=\dfrac{66}{67}\)
\(\dfrac{1}{1\times2}+\dfrac{2}{2\times4}+\dfrac{3}{4\times7}+\dfrac{4}{7\times11}+....+\dfrac{11}{56\times67}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+....+\dfrac{1}{56}-\dfrac{1}{67}\)
\(=1-\dfrac{1}{67}\)
\(=\dfrac{1}{66}\)
1/1x2 + 2/2x4 + 3/4x7 + 4/7x11 +......+ 11/56x67
biể thức trên = 1/1 - 1/2 + 1/2 - 1/4 + 1/7 +.....+ 1/11 - 1/67
= 1/1 - 1/67 = 66/67
a=1/1x2+1/2x4+1/4x7+1/7x11+.....+10/46x56
Help meeee !
Tính tổng của phép tính sau :
1/1x2 + 2/2x4 + 3/4x7 + 4/7x11 +...+ 8/29x37 + 9/37x46 = ?
Hỡi các thiên tài toán học, hãy giúp mình lần này !
Trân trọng cảm ơn
1/1x2 + 2/2x4 + 3/4x7 + 4/7x11 +...+ 8/29x37 + 9/37x46
=2-1/1x2+4-2/2x4+...+46-37/37x46
=1-1/2+1/2-1/4+...+1/37-1/46
=1-1/46
=45/46
`#``\text{Lócc}`
`***` chấm là nhân.
\(\dfrac{1}{1.2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+\dfrac{4}{7.11}+...+\dfrac{8}{29.37}+\dfrac{9}{37.46}\\ =\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+..+\dfrac{1}{29}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{46}\\ =\dfrac{1}{1}-\dfrac{1}{46}\\ =\dfrac{46}{46}-\dfrac{1}{46}\\ =\dfrac{45}{46}\)
tính tổng
S= \(\frac{4}{1+2}\)+\(\frac{4}{1+2+3}\)+\(\frac{4}{1+2+3+4}\)+...+\(\frac{4}{1+2+3+...+100}\)
O=\(\frac{1}{1x2}\)+\(\frac{2}{2x4}\)+\(\frac{3}{4x7}\)+\(\frac{4}{7x11}\)+\(\frac{5}{11x16}\)
X=\(\frac{3}{54}\)+\(\frac{5}{126}\)+\(\frac{7}{294}\)+\(\frac{8}{609}\)
giúp mình nha
Ai nhanh mình sẽ tick
A=5/1x6+5/6x11+5/11x16+5/16x21+...+5/101x106
B=3/1x4+3/4x7+3/7x10+....+3/97x100
C=1/2x7+1/7x12+1/12x17+....+1/97x102
D=1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
E=3/2x4+3/4x6+3/6x8+....+3/98x100
A = \(\dfrac{5}{1.6}\)+\(\dfrac{5}{6.11}\)+\(\dfrac{5}{11.16}\)+\(\dfrac{5}{16.21}\)+...+\(\dfrac{5}{101.106}\)
A = \(\dfrac{1}{1}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{106}\)
A = \(\dfrac{105}{106}\)
B = \(\dfrac{3}{1.4}\) +\(\dfrac{3}{4.7}\)+\(\dfrac{3}{7.10}\)+...+\(\dfrac{3}{97.100}\)
B = \(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{97}-\dfrac{1}{100}\)
B = \(\dfrac{1}{1}\) - \(\dfrac{1}{100}\)
B = \(\dfrac{99}{100}\)
C = \(\dfrac{1}{2.7}+\dfrac{1}{7.12}\) + \(\dfrac{1}{12.17}\)+...+ \(\dfrac{1}{97.102}\)
C= \(\dfrac{1}{5}\) \(\times\)( \(\dfrac{5}{2.7}+\dfrac{5}{7.12}+\dfrac{5}{12.17}+...+\dfrac{5}{97.102}\))
C = \(\dfrac{1}{5}\)\(\times\)(\(\dfrac{1}{2}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{12}\) + \(\dfrac{1}{12}\) - \(\dfrac{1}{17}\)+...+ \(\dfrac{1}{97}\) - \(\dfrac{1}{102}\))
C = \(\dfrac{1}{5}\) \(\times\)( \(\dfrac{1}{2}\) - \(\dfrac{1}{102}\))
C = \(\dfrac{1}{5}\) \(\times\) \(\dfrac{25}{51}\)
C = \(\dfrac{5}{51}\)
D = \(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) + \(\dfrac{1}{42}\) + \(\dfrac{1}{56}\) + \(\dfrac{1}{72}\)
D = \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\)+\(\dfrac{1}{7.8}\)+ \(\dfrac{1}{8.9}\)
D = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\)+\(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\) - \(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{8}\)+\(\dfrac{1}{8}\)-\(\dfrac{1}{9}\)
D = \(\dfrac{1}{1}\) - \(\dfrac{1}{9}\)
D = \(\dfrac{8}{9}\)
E = \(\dfrac{3}{2.4}\)+\(\dfrac{3}{4.6}\)+\(\dfrac{3}{6.8}\)+...+\(\dfrac{3}{98.100}\)
E = \(\dfrac{3}{2}\) \(\times\) ( \(\dfrac{2}{2.4}\) + \(\dfrac{2}{4.6}\)+ \(\dfrac{2}{6.8}\)+...+\(\dfrac{2}{98.100}\))
E = \(\dfrac{3}{2}\)\(\times\)( \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\)+ \(\dfrac{1}{4}\) - \(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)-\(\dfrac{1}{8}\)+...+\(\dfrac{1}{98}\) - \(\dfrac{1}{100}\))
E = \(\dfrac{3}{2}\) \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{100}\))
E = \(\dfrac{3}{2}\) \(\times\) \(\dfrac{49}{100}\)
E = \(\dfrac{147}{200}\)