Tính:
D=\(\frac{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{999}-\frac{1}{1000}}{500-\frac{500}{501}-\frac{501}{502}-.....-\frac{999}{1000}}\)
Tính nhanh: \(A=\frac{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}}{500-\frac{500}{501}-\frac{501}{502}-\frac{502}{503}-...-\frac{999}{1000}}\)
\(\frac{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}}{500-\frac{500}{501}-\frac{501}{502}-...-\frac{999}{1000}}=\frac{\left(1-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{999}-\frac{1}{1000}\right)}{500-\left(1-\frac{1}{501}\right)-\left(1-\frac{1}{502}\right)-...-\left(1-\frac{1}{1000}\right)}\)
hình như cái mẫu bạn ghi dấu sai thì phải, còn tử thì mình lười làm lắm
tử bạn tính ra 1/2+1/12+...+1/999 000 sau đó phân tích ra là
khó thật
nhớ L-I-K-E nhe tại vì cậu bảo giúp mình, mình cho đúng liền
\(B=\frac{\frac{2016}{1000}+\frac{2016}{999}+\frac{2016}{998}+.....+\frac{2016}{501}}{\frac{-1}{1\cdot2}-\frac{1}{3\cdot4}-\frac{1}{5\cdot6}-.....-\frac{1}{999\cdot1000}}\)
\(B=\frac{\frac{2016}{1000}+\frac{2016}{999}+\frac{2016}{998}+...+\frac{2016}{501}}{-\frac{1}{1\cdot2}-\frac{1}{3\cdot4}-\frac{1}{5\cdot6}-...-\frac{1}{999\cdot1000}}\)
\(B=\frac{2016\left(\frac{1}{1000}+\frac{1}{999}+\frac{1}{998}+...+\frac{1}{501}\right)}{-\left(\frac{1}{1\cdot2}+\frac{1}{3\cdot4}+\frac{1}{5\cdot6}+...+\frac{1}{999\cdot1000}\right)}\)
\(B=\frac{2016\left(\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+...+\frac{1}{1000}\right)}{-\left(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{999}-\frac{1}{1000}\right)}\)
\(B=\frac{2016\left(\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+...+\frac{1}{1000}\right)}{-\left[\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{1000}\right)\right]}\)
\(B=\frac{2016\left(\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+...+\frac{1}{1000}\right)}{-\left[\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1000}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{1000}\right)\right]}\)
\(B=\frac{2016\left(\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+...+\frac{1}{1000}\right)}{-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1000}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{500}\right)}\)
\(B=\frac{2016\left(\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+...+\frac{1}{1000}\right)}{-\left(\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+...+\frac{1}{1000}\right)}\)
\(B=\frac{2016}{-1}=-2016\)
Chứng minh rằng :
1 - \(\frac{1}{2}\)+\(\frac{1}{3}\) - \(\frac{1}{4}\) + \(\frac{1}{5}\) - \(\frac{1}{6}\)+ . . . + \(\frac{1}{999}\)-\(\frac{1}{1000}\) = \(\frac{1}{501}\)+ \(\frac{1}{502}\)+\(\frac{1}{503}\) + . . . + \(\frac{1}{1000}\)
1-1/2+1/3-1/4+......+1/999-1/1000
500-500/501-501/502-502/503-....-999/1000
các bạn ơi giúp nhanh nha mình đang cần rất gấp
So sánh :A=1-1/2+1/3-1/4+...+1/999-1/1000 và B=500-500/501-501/502-502/503-...-999/1000
Câu 1: Không quy đồng hãy so sánh :
\(\frac{17171718}{19191920}\) và \(\frac{33}{38}\)
Câu 2: Chứng tỏ rằng :
\(\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{999}-\frac{1}{1000}=\frac{1}{501}+\frac{1}{502}+.......+\frac{1}{1000}\)
Câu 3: Tìm x :
\(\frac{3}{4}x-\frac{4}{3}x-\frac{1}{12}x+\frac{7}{48}=0\)
Chứng minh rằng :
1 - \(\frac{1}{2}\)+ \(\frac{1}{3}\)-\(\frac{1}{4}\)+ \(\frac{1}{5}\)- \(\frac{1}{6}\)+ . . . + \(\frac{1}{999}\)- \(\frac{1}{1000}\)= \(\frac{1}{501}\)+ \(\frac{1}{502}\)+\(\frac{1}{503}\)+ . . . + \(\frac{1}{1000}\)
rút gọn bằng cách thay số bằng chữ:
H=\(4\frac{7}{1000}.\frac{1}{999}-1\frac{1}{500}.\frac{4}{999}+\frac{1001}{999.1000}\)
Tính:
\(\left(\frac{1000}{1}+\frac{999}{2}+\frac{998}{3}+\frac{997}{4}+...+\frac{2}{999}+\frac{1}{1000}\right)\)\(:\)\(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{1000}\right)\)