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a) Giải
So sánh từng số hạng của A với B, ta thấy:
\(\dfrac{19}{41}< \dfrac{21}{41};\dfrac{23}{53}< \dfrac{23}{49}\) và \(\dfrac{29}{61}< \dfrac{33}{65}\) (vì 29.65 < 33.61)
\(\Rightarrow\dfrac{19}{41}+\dfrac{23}{53}+\dfrac{29}{61}< \dfrac{21}{41}+\dfrac{23}{49}+\dfrac{33}{65}\)
\(\Rightarrow A< B\)
Vậy A < B
b) Giải
Ta có: \(C=\dfrac{19^{20}+5}{19^{20}-8}=\dfrac{19^{20}-8+13}{19^{20}-8}=1+\dfrac{13}{19^{20}-8}\)
\(D=\dfrac{19^{21}+6}{19^{21}-7}=\dfrac{19^{21}-7+13}{19^{21}-7}=1+\dfrac{13}{19^{21}-7}\)
Vì \(19^{20}-8< 19^{21}-7\) và \(13>0\)
\(\Rightarrow\dfrac{13}{19^{20}-8}< \dfrac{13}{19^{21}-7}\)
\(\Rightarrow1+\dfrac{13}{19^{20}-8}< 1+\dfrac{13}{19^{21}-7}\)
\(\Rightarrow\) \(C< D\)
Vậy C < D.
A=3/2+13/12+31/30+...+9901/9900
= 1+1/2+1+1/12+1+1/30+...+1+1/9900
=1+1+1+...+1+1(50 cs)+1/2+1/12+1/30+...+1/9900
=50+1/2+1/12+1/30+...+1/9900
B=5/6+19/20+41/42+...+10099/10100
=(1-1/6)+(1-1/20)+(1-1/42)+...+(1-1/10100)
=1+1+...+1(50cs)-1/6-1/20-1/42-...-1/10100
A-B=(50+1/2+1/12+1/30+...+1/9900)-(50-1/6-1/20-1/42-...-1/10100)
=1/2+1/6+1/12+1/20+...+1/9900+1/10100
=1/1.2+1/2.3+1/3.4+1/4.5+...+1/99.100+1/100.101
=1-1/2+1/2-1/3+1/3-1/4+1/4-...+1/99-1/100+1/100-1/101
=1-1/101
=100/101
A=1
B=-3/4
C=-1139/3731
a) 1
b)-111
c)61/91
nhầm, câu c=-1139/3731; câu b=-3/4
a, \(\frac{7}{19}+\frac{12}{19}=\frac{7+12}{19}=\frac{19}{19}=1\)
b, \(\frac{-48}{96}+\frac{-37}{148}=-\frac{1}{2}-\frac{1}{4}=\frac{-2}{4}-\frac{1}{4}=\frac{-2-1}{4}=-\frac{3}{4}\)
c, \(VP=\frac{5}{13}-\frac{5}{7}-\frac{20}{41}+\frac{21}{41}=\frac{5}{13}-\frac{5}{7}+\frac{1}{41}=\frac{35-65}{91}+\frac{1}{41}\)
\(=-\frac{30}{91}+\frac{1}{41}=-\frac{1139}{3731}\)
\(a,\frac{7}{19}+\frac{12}{19}=\frac{7+12}{19}=\frac{19}{19}=1\)
\(b,\frac{-48}{96}+\frac{-37}{148}=\frac{-1}{2}+\frac{-1}{4}=\frac{-4}{8}+\frac{-2}{8}=\frac{-6}{8}=\frac{-3}{4}\)
\(c,\frac{5}{13}+\frac{-5}{7}+\frac{-20}{41}-\frac{-21}{41}\)
\(=0+\frac{1}{41}=\frac{1}{41}\)
a)7/19+12/19=7+12/19=19/19=1
b)-48/96+-37/148=-1/2+-1/4=-2/4+-1/4=-3/4
c)
a)7/19 + 12/19 = 7 + 12/19= 19/19 = 1 b)-48/96 + -37/148 = -1/2 + -1/4 = -2/4 + -1/4= -3/4 c)A=5/13 + -5/7 + -20/41 - -21/41 = -30/91 + 1 = 61/91 Ngọc chúc bn hok tốt nha / $$$
dễ ma ko biet lam
a)7/19+12/19=19/19=1
b)-48/96+37/148=(-1)/2 + 1/4 = (-1)/4
c) 5/13+ -5/7 + - 20/41 - (-20/41) = -30/91 + (-1)= (-121/91)