Tính nhanh . a) 1/90 + 1/72+ 1/ 110 + .....+1/9702+1/9900
Tính nhanh . a) 1/90 + 1/72+ 1/ 110 + .....+1/9702+1/9900
1/72+ 1/90 + 1/ 110 + .....+1/9702+1/9900
= 1/ 8x9 + 1/9x10+1/10x11+.....+1/98x99+1/99x100
.....
= 1/8 - 1/100
=23/200
Tính nhanh
1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
9/20 - 11/30 + 13/42 - 15/56 + 17/72 - ........ + 197/9702 - 199/9900
\(A=\frac{1}{72}+\frac{1}{90}+........+\frac{1}{9702}+\frac{1}{9900}\)
\(B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
giải nhanh giùm mk nha (nhớ là có lời giải đấy)
Tính T=1/2+1/6+1/12+1/20+1/30+....+1/9702+1/9900
T= 1 - 1/2 + 1/2 - 1/3 + ......+ 1/99 - 1/100
= 1 - 1/100
= 99/100
Tính t =1/2+1/6+1/12+1/20+1/30+...........+1/9702+1/9900
\(t=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(t=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(t=1-\frac{1}{100}=\frac{99}{100}\)
Vậy \(t=\frac{99}{100}\)
Tính T biết : 1/2+1/6+1/12+1/20+1/30+.........+1/9702+1/9900
tính nhanh
1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
\(\dfrac{1}{20}=\dfrac{1}{4x5}=\dfrac{1}{4}-\dfrac{1}{5}\)
Tương tự các phân số khác
S= \(\dfrac{1}{4}-\dfrac{1}{12}=\dfrac{1}{6}\)
\(\dfrac{1}{20}+\dfrac{1}{30}\)+ \(\dfrac{1}{42}\)+\(\dfrac{1}{56}\)+\(\dfrac{1}{72}\)+\(\dfrac{1}{90}\)+\(\dfrac{1}{110}\)+\(\dfrac{1}{132}\)
= \(\dfrac{1}{4\times5}\)+\(\dfrac{1}{5\times6}\)+\(\dfrac{1}{6\times7}\)+\(\dfrac{1}{7\times8}\)+\(\dfrac{1}{8\times9}\)+\(\dfrac{1}{9\times10}\)+\(\dfrac{1}{10\times11}\)+\(\dfrac{1}{11\times12}\)
= \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)-\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{8}\)+\(\dfrac{1}{8}\)-\(\dfrac{1}{9}\)+\(\dfrac{1}{9}\)-\(\dfrac{1}{10}\)+\(\dfrac{1}{10}\)-\(\dfrac{1}{11}\)+\(\dfrac{1}{11}\)-\(\dfrac{1}{12}\)
= \(\dfrac{1}{4}\) - \(\dfrac{1}{12}\)
= \(\dfrac{3}{12}\) - \(\dfrac{1}{12}\)
= \(\dfrac{2}{12}\)
=\(\dfrac{1}{6}\)
=1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10+1/10x11+1/11x12
=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12
=1/4-1/12=3/12-1/12=2/12=1/6
Tính nhanh:
1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132
`=1/[4xx5]+1/[5xx6]+1/[6xx7]+...+1/[11xx12]`
`=1/4-1/5+1/5-1/6+1/6-1/7+...+1/11-1/12`
`=1/4-1/12=3/12-1/12=2/12=1/6`
\(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\\ =\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}+\dfrac{1}{10\times11}+\dfrac{1}{11\times12}\\ =\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}\\ =\dfrac{1}{4}-\dfrac{1}{12}\\ =\dfrac{3}{12}-\dfrac{1}{12}=\dfrac{2}{12}=\dfrac{1}{6}\)
tính T = 1/2 +1/6+1/12+1/20+1/30+...+1/9702+1/9900
T=
ta có : t = 1/1.2 + 1/2.3 + 1/3.4 + .... + 1/98.99 + 1/99.100
=> t = 1/1 - 1/2 + 1/2 - 1/3 + .... + 1/99 - 1/100
=> t = 1 - 1/100
=> t = 99/100
T=1/1x2+1/2x3+1/3x4+....................+1/98x99+1/99x100
T=1-1/2+1/2-1/3+..............+1/98-1/99+1/99-1/100
T=1-1/100
T=99/100