S=3/2+7/6+13/12+21/20+...+133/13
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3/2+7/6+13/12+21/20+...+133/132
=1+ 1/2 + 1+ 1/6 + 1+ 1/12 + 1+ 1/20+......+ 1+ 1/132
=(1+ 1 + 1+.....+ 1) + ( 1/2+ 1/6+1/12+ 1/20+....+ 1/132)
= 11+ ( 1/1×2+ 1/2×3+1/3×4+1/4×5+.....+1/11×12)
=11+ ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/11-1/12)
=11+(1-1/12)
= 11+11/12
=143/12
3/2+7/6+13/12+21/20+...+133/132 =1+ 1/2 + 1+ 1/6 + 1+ 1/12 + 1+ 1/20+......+ 1+ 1/132 =(1+ 1 + 1+.....+ 1) + ( 1/2+ 1/6+1/12+ 1/20+....+ 1/132) = 11+ ( 1/1×2+ 1/2×3+1/3×4+1/4×5+.....+1/11×12) =11+ ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/11-1/12) =11+(1-1/12) = 11+11/12 =143/12
5.\(-\dfrac{3}{7}+\dfrac{5}{13}+\dfrac{-4}{12}=-\dfrac{103}{273}\)
b.\(-\dfrac{5}{21}+\dfrac{-2}{21}+\dfrac{8}{24}=\dfrac{-5-2}{21}+\dfrac{8}{24}=-\dfrac{7}{21}+\dfrac{8}{24}=-\dfrac{1}{3}+\dfrac{8}{24}=0\)
c.\(\dfrac{5}{13}+\dfrac{-5}{7}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-21}{41}=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(\dfrac{-20}{41}+\dfrac{-21}{41}\right)+-\dfrac{5}{7}=1-1-\dfrac{5}{7}=-\dfrac{5}{7}\)
c) Ta có: \(\dfrac{3}{5}+\dfrac{-5}{20}+\dfrac{30}{75}+\dfrac{-7}{4}\)
\(=\dfrac{3}{5}+\dfrac{2}{5}+\dfrac{-1}{4}+\dfrac{-7}{4}\)
\(=1-2=-1\)
Giải:
a)-1/12+4/3=-1/12+16/12=15/12=5/4
b)(-4/14-3/15)-(1/5-20/35-(-1)).7
=-17/35-22/35.7
=-17/35-22/5
=-171/35
c)3/5+-5/20+30/75+-7/4
=3/5+-1/4+2/5+-7/4
=(3/5+2/5)+(-1/4+-7/4)
=1+-2
=-1
d)5/6.-12/14+7/13
=-5/7+7/13
=-16/91
e)2/-9-5/-36-1/4
=-1/12-1/4
=-1/3
f)2/23+-5/12+7/18+21/23+-7/12
=(2/23+21/23)+(-5/12+-7/12)+7/18
=1+-1+7/18
=7/18
12) 17 – 11 – 14 – (-39)
=17-11-14+39
=6-14+39
=-8+39
=31
13) −127 - 18.( 5 - 6)
=-127-18.1
=-145
14) 100 + (+430) + 2145 + (-530)
=530+2145-530
=(530-530)+2145
=0+2145
=2145
15) (+12).13 + 13.(-22)
=13.[12+(-22)]
=13.(-10)
=-130
16) {[14 : (-2)] + 7} : 2012
={-7+7}:2012
=0:2012
=0
17) 13 – 18 – (- 42) - 15
=13-18+42-15
=-5+42-15
=37-15
=22
18) 369 – 4[(-5) + 4.(-8)]
=369-4[-5+(-32)]
=369-4(-37)
=369+148
=517
19) (-12).(-13) +13.(-29)
=12.13+13.(-29)=13.[12+(-29)]=13.(-17)=-221
20) 125 – 4[ 3 – 7.(-2) ]
=125-4[3+14]
=125-4.17
=125-68
=57
21) (-14).9 – 13.(-9)
=(-14).9+13.9
=9.[-14+13]
=9.(-1)
=-9
S=\(\dfrac{3}{2}+\dfrac{7}{6}+\dfrac{13}{12}+\dfrac{21}{20}+...+\dfrac{133}{132}\)
=\(\left(1+\dfrac{1}{2}\right)+\left(1+\dfrac{1}{6}\right)+\left(1+\dfrac{1}{12}\right)+\left(1+\dfrac{1}{20}\right)+...+\left(1+\dfrac{1}{132}\right)\)
=(1+1+1+1+1+1+1+1+1+1+1)+\(\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{132}\right)\)
=11+\(\left(\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+...+\dfrac{1}{11x12}\right)\)
=11+\(\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{11}-\dfrac{1}{12}\right)\)
=11+\(\left(\dfrac{1}{1}-\dfrac{1}{12}\right)\)
=11+\(\dfrac{11}{12}\)
=\(\dfrac{143}{12}\)
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