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\(A=\left(1-\frac{1}{2018}\right)\left(1-\frac{2}{2018}\right)\left(1-\frac{3}{2018}\right)...\left(1-\frac{2020}{2018}\right).\)
\(=\frac{2017}{2018}\cdot\frac{2016}{2018}\cdot\frac{2015}{2018}\cdot...\cdot\left(1-\frac{2018}{2018}\right)\cdot...\cdot\frac{-2}{2018}\)
\(=\frac{2017}{2018}\cdot\frac{2016}{2018}\cdot\frac{2015}{2018}\cdot...\cdot0\cdot...\cdot\frac{-2}{2018}\)
\(=0\)
Hello Triệu Mẫn điên .Tui là Nguyên 6n1^^
Tui đang suy nghĩ
Tui biết làm nhưng không nói
chỉ nói kết quả bằng 10
\(B=1+\frac{1}{2}.\frac{\left(1+2\right).2}{2}+\frac{1}{3}.\frac{\left(1+3\right).3}{2}+...+\frac{1}{2018}.\frac{\left(1+2018\right).2018}{2}\)
\(=1+\frac{3}{2}+\frac{4}{2}+...+\frac{2019}{2}=1+\frac{3+4+...+2019}{2}=1+\frac{\left(3+2019\right)2017}{2}=2039188\)
\(=\frac{12}{7}\cdot\frac{3}{4}-\frac{6}{7}\cdot\frac{4}{3}+\frac{6}{7}\)
\(=\frac{6}{7}\left(\frac{3}{2}-\frac{4}{3}+1\right)\)
\(=\frac{6}{7}\left(\frac{1}{6}+1\right)=\frac{6}{7}\cdot\frac{7}{6}=1\)
2.
\(=2017\cdot2018\cdot\left[\left(2016\cdot2018\right)-\left(2016\cdot2017\right)\right]\)
\(=2017\cdot2018\cdot2016\left(2018-2017\right)=2016\cdot2017\cdot2018\)
3.
\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)....\left(\frac{1}{100}-1\right)=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot....\cdot\frac{99}{100}\)
\(=\frac{1}{100}\)
4.
\(=\frac{1+2+2^2+2^4+...+2^9}{2\left(1+2+2^2+2^3+2^4+...+2^9\right)}\)
\(=\frac{1}{2}\)
mình chỉ làm được câu 3 thôi
có \(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)....\left(\frac{1}{100}-1\right)\)
\(=\frac{-1}{2}\times\frac{-2}{3}\times....\times\frac{-99}{100}\)
\(=\frac{\left(-1\right)\left(-2\right)....\left(-99\right)}{2\times3\times....\times100}\)
\(=\frac{-\left(1\times2\times....\times99\right)}{2\times3\times....\times100}\)
\(=\frac{-1}{100}\)
\(\left(\frac{1}{4}-\frac{1}{5}-\frac{1}{20}\right)\left(\frac{2017}{2018}-\frac{2018}{2019}\right)\)
= \(\left(\frac{1}{20}-\frac{1}{20}\right)\left(\frac{2017}{2018}-\frac{2018}{2019}\right)\)
= \(0\cdot\left(\frac{2017}{2018}-\frac{2018}{2019}\right)=0\)
Đặt \(\frac{2017}{2018}-\frac{2018}{2019}=A\)
Ta có :
\(\left(\frac{1}{4}-\frac{1}{5}-\frac{1}{20}\right)\left(\frac{2017}{2018}-\frac{2018}{2019}\right)\)
\(=\left(\frac{5}{20}-\frac{4}{20}-\frac{1}{20}\right).A\)
\(=\left(\frac{1}{20}-\frac{1}{20}\right).A\)
\(=0.A\)
\(=0\)
Vậy ...
Chúc bạn học tốt !!!