1+2-2+3-...-999+1000=?
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31 tháng 3 2018
\(A=\dfrac{1000-\left(1+\dfrac{1}{2}+...+\dfrac{1}{999}+\dfrac{1}{1000}\right)}{\dfrac{1}{2}+\dfrac{2}{3}+...+\dfrac{998}{999}+\dfrac{999}{1000}}\)
\(A=\dfrac{1000-1-\dfrac{1}{2}-\dfrac{1}{3}...-\dfrac{1}{999}-\dfrac{1}{1000}}{\dfrac{1}{2}+\dfrac{2}{3}+...+\dfrac{998}{999}+\dfrac{999}{1000}}\)
\(A=\dfrac{99-\dfrac{1}{2}-\dfrac{1}{3}...-\dfrac{1}{999}-\dfrac{1}{1000}}{\dfrac{1}{2}+\dfrac{2}{3}+...+\dfrac{998}{999}+\dfrac{999}{1000}}\)
\(A=\dfrac{\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{3}\right)+...+\left(1-\dfrac{1}{999}\right)+\left(1-\dfrac{1}{1000}\right)}{\dfrac{1}{2}+\dfrac{2}{3}+...+\dfrac{998}{999}+\dfrac{999}{1000}}\)
\(A=\dfrac{\dfrac{1}{2}+\dfrac{2}{3}+...+\dfrac{998}{999}+\dfrac{999}{1000}}{\dfrac{1}{2}+\dfrac{2}{3}+...\dfrac{998}{999}+\dfrac{999}{1000}}\)
\(A=1\)
XO
29 tháng 1 2020
\(B=\frac{\frac{2016}{1000}+\frac{2016}{999}+...+\frac{2016}{501}}{\frac{-1}{1.2}+\frac{-1}{3.4}+...+\frac{-1}{999.1000}}=\frac{2016.\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{999.1000}\right)}\)
\(=\frac{2016.\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}\right)}\)
\(=\frac{2016\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left[\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{999}+\frac{1}{1000}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{1000}\right)\right]}\)
\(=\frac{2016.\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left[\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{999}+\frac{1}{1000}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{500}\right)\right]}\)
\(=\frac{2016.\left(\frac{1}{1000}+\frac{1}{999}+...+\frac{1}{501}\right)}{-\left(\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+....+\frac{1}{999}+\frac{1}{1000}\right)}=\frac{2016}{-1}=-2016\)
Vậy B = - 2016
29 tháng 1 2020
Bạn Xyz cho mik hỏi ở phần mẫu số tại sao lại có -2*(1/2+1/4+...+1/1000) vậy? Nó ở đâu ra thế?
=1+1000=1001
= 1+0+0+0+...+1000 vì 2-2 = 0 ; 3-3 = 0
=> 1001