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\(P=\frac{2.3.4-2.3.4.9+2.3.4.11-2.3.4.13}{5.6.7-5.6.7.9+5.6.7.13}\)
\(=\frac{2.3.4.\left(1-9+11-13\right)}{5.6.7.\left(1-9+11-13\right)}=\frac{2.3.4}{5.6.7}=\frac{24}{210}=\frac{4}{35}\)
\(P=\frac{2.3.4-2.3.4.9+2.3.4.11-2.3.4.13}{5.6.7-5.6.7.9+5.6.7.11-5.6.7.13}=\frac{2.3.4.\left(1-9+11-13\right)}{5.6.7.\left(1-9+11-13\right)}=\frac{2.3.4}{5.6.7}=\frac{24}{210}=\frac{4}{35}\)
BÀI NÈ KO KHÓ
1,
Vì \(\dfrac{a}{b}=\dfrac{-8}{11}\)
=>a.11=b.(-8) (1)
Mà b-a=190
=>b=a+190 (2)
Từ (1), (2)
=>a.11=(a+190).(-8)
=>11a=(-8).a+190.(-8)
=>11a=-8.a+(-1520)
=>11a+8a=-1520
=>a.(11+8)=-1520
=>a.19=-1520
=>a=(-1520):19
=>a=-80
=>b=-80+190=110
Vậy a=-80;b=110
Câu 1:
Ta có:
\(\dfrac{a}{b}=\dfrac{-8}{11}\Leftrightarrow1-\dfrac{a}{b}=1-\dfrac{-8}{11}\)
Hay \(\dfrac{b-a}{b}=\dfrac{11+8}{11}\left(1\right)\)
Thay \(b-a=190\) vào \(\left(1\right)\) ta được:
\(\dfrac{190}{b}=\dfrac{19}{11}\Leftrightarrow b=110\Leftrightarrow a=-80\)
Vậy phân số \(\dfrac{a}{b}=\dfrac{-80}{110}\)
Câu 2: Ta có:
\(P=\dfrac{2.3.4-2.3.4.9+2.3.4.11-2.3.4.13}{5.6.7-5.6.7.9+5.6.7.11-5.6.7.13}\)
\(=\dfrac{2.3.4.\left(1-9+11-13\right)}{5.6.7.\left(1-9+11-13\right)}\)
\(=\dfrac{2.3.4}{5.6.7}=\dfrac{4}{35}\)
Vậy \(P=\dfrac{4}{35}\)
Câu 3:
\(S=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}\)
\(\Rightarrow2S=2\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}\right)\)
\(=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{19}}\)
Do đó \(2S-S=1-\dfrac{1}{2^{20}}\) Hay:
\(S=1-\dfrac{1}{2^{20}}< 1\) (Đpcm)
Ta có P=\(\frac{2.3.4\left(1-9-11-13\right)}{5.6.7\left(1-9-11-13\right)}\)=\(\frac{2.3.4}{5.6.7}\)=\(\frac{4}{35}\)
Chúc bạn hok tốt !
P= \(\dfrac{2.3.4-2.3.4.9+2.3.4.11+2.3.4.13}{5.6.7-5.6.7.9+5.6.7-5.6.7.13}\)
P= \(\dfrac{2.3.4.\left(1-9+11+13\right)}{5.6.7.\left(1-9+11+13\right)}\)
P= \(\dfrac{2.3.4}{5.6.7}\)
P= \(\dfrac{4}{5.7}\)
P= \(\dfrac{4}{35}\)
Bài 1 :
Ta có : \(\frac{2.3.4-2.3.4.9+2.3.4.9.11-2.3.4.13}{5.6.7-5.6.7.9+5.6.7.11-5.6.7.13}=\frac{2.3.4.\left(1-9+11-13\right)}{5.6.7.\left(1-9+11-13\right)}=\frac{2.3.4}{5.6.7}=\frac{4}{35}\)
Bài 2 :
Ta có \(\frac{a}{b}=\frac{-8}{11}\Rightarrow a.11=-8.b\)
mà b - a = 190 => b = a+190
=> \(a.11=-8.\left(a+190\right)\Rightarrow a.11=-8.a-1520\)
=> \(a.11-\left(-8.a\right)=1520\Rightarrow a.11+8.a=1520\Rightarrow a.19=1520\)
=> \(a=80\) và \(b=80+190=270\)
Vậy \(\frac{a}{b}=\frac{80}{270}\)