Tính nhanh :
254 . 399 - 145
254+399x253
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A = \(\dfrac{254\times399-145}{254+399\times253}\)
A = \(\dfrac{\left(253+1\right)\times399-145}{254+399\times253}\)
A = \(\dfrac{253\times399+399-145}{254+399\times253}\)
A = \(\dfrac{253\times399+254}{254+399\times253}\)
A = 1
a) \(254x399-145=\left(250+4\right)\left(400-1\right)-145\)
\(=100000+1600-250-145-4=101600-\left(250+145+4\right)\)
\(=101600-399=101201\)
b) \(254+399x253=254+\left(400-1\right)x\left(250+3\right)\)
\(=254+100000+1200-250-3\)
\(=101454-250-3=101201\)
\(\frac{254.399-145}{254+399.253}\)
\(=\frac{253.399+399-145}{254+399.253}\)
\(=\frac{253.399+254}{254+399.253}=1\)
\(\frac{254.399-145}{254+399.253}=\frac{\left(253+1\right).399-145}{254+399.253}=\frac{253.399+399-145}{254+399.253}=\frac{253.399+254}{254+399.253}=1\)
ghép đầu cuối dăt chung 399 ra ngoài
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\(\frac{254+399.253}{399.254-145}\)
\(=\frac{254+399.253}{399.\left(253+1\right)-145}\)
\(=\frac{254+399.253}{399.253+399.1-145}\)
\(=\frac{254+1}{1+399-145}=1\)
Chúc bạn học tốt!!!
C=\(\frac{1}{2}.\frac{2}{3}.......\frac{2016}{2017}\)
C= CÂU HỎI TƯƠNG TỰ
=> đcpm
\(A=\frac{254\cdot399-145}{254+399\cdot253}\)
\(A=\frac{\left(253+1\right)\cdot399-145}{254+399\cdot253}\)
\(A=\frac{253\cdot399+\left(399-145\right)}{254+399\cdot253}\)
\(A=\frac{253\cdot399+254}{254+399\cdot253}\)
\(A=1\)
\(B=\frac{5932+6001\cdot5931}{5932\cdot6001-69}\)
\(B=\frac{5932+6001\cdot5931}{\left(5931+1\right)\cdot6001-69}\)
\(B=\frac{5932+6001\cdot5931}{5931\cdot6001+\left(6001-69\right)}\)
\(B=\frac{5932+6001\cdot5931}{5931\cdot6001+5932}\)
\(B=1\)
\(C=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot...\cdot\left(1-\frac{1}{2017}\right)\)
\(C=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{2016}{2017}\)
\(C=\frac{1\cdot2\cdot3\cdot...\cdot2016}{2\cdot3\cdot4\cdot...\cdot2017}\)
\(C=\frac{1}{2017}\)
= ( 253 + 1) . 399 - 145
254 + 399 x 253
= 253 . 399 + 1 . 399 - 145
254 + 399 x 253
= 253 . 399 + 254
254 + 399 . 253
= 1
\(\frac{254.399-145}{254+399.253}=\frac{253.399+399-145}{399.253+254}=\frac{253.399+254}{399.253+154}=1\)