Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(a,\frac{1}{999\cdot1000}-\frac{1}{998\cdot999}-\frac{1}{997\cdot998}-...-\frac{1}{2\cdot1}\)
\(=\frac{1}{999\cdot1000}-\left[\frac{1}{2\cdot1}+\frac{1}{2\cdot3}+...+\frac{1}{997\cdot998}+\frac{1}{998\cdot999}\right]\)
\(=\frac{1}{999\cdot1000}-\left[1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{998}-\frac{1}{999}\right]\)
\(=\frac{1}{999\cdot1000}-\left[1-\frac{1}{999}\right]=\frac{1}{999\cdot1000}-\frac{998}{999}=...\)
Tính nốt , không chắc :v
a; - \(\dfrac{2}{3}\) + \(\dfrac{3}{4}\) - (- \(\dfrac{1}{6}\)) + (- \(\dfrac{2}{5}\))
= - \(\dfrac{2}{3}\) + \(\dfrac{3}{4}\) + \(\dfrac{1}{6}\) - \(\dfrac{2}{5}\)
= \(-\dfrac{40}{60}\) + \(\dfrac{45}{60}\) + \(\dfrac{10}{60}\) - \(\dfrac{24}{60}\)
= \(\dfrac{5}{60}\) + \(\dfrac{10}{60}\) - \(\dfrac{24}{60}\)
= \(\dfrac{15}{60}\) - \(\dfrac{24}{60}\)
= - \(\dfrac{3}{20}\)
b; (- \(\dfrac{2}{3}\)) + (- \(\dfrac{1}{5}\)) + \(\dfrac{3}{4}\) - \(\dfrac{5}{6}\) - \(\dfrac{-7}{10}\)
= - \(\dfrac{2}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{3}{4}\) - \(\dfrac{5}{6}\) + \(\dfrac{7}{10}\)
= - \(\dfrac{40}{60}\) - \(\dfrac{12}{60}\) + \(\dfrac{45}{60}\) - \(\dfrac{50}{60}\) + \(\dfrac{42}{60}\)
= - \(\dfrac{52}{60}\) + \(\dfrac{45}{60}\) - \(\dfrac{50}{60}\) + \(\dfrac{42}{60}\)
= - \(\dfrac{7}{60}\) - \(\dfrac{50}{60}\) + \(\dfrac{42}{60}\)
= - \(\dfrac{57}{60}\) + \(\dfrac{42}{60}\)
= - \(\dfrac{1}{4}\)
`a, 1/2 +1/3 +1/4`
`= 6/12 + 4/12 + 3/12`
`= (6+4+3)/12`
`= 13/12`
`b,5/2 -1/3 +1/4`
`= 30/12 - 4/12 + 3/12`
`=(30-4+3)/12`
`= 29/12`
`c, 1/2 . 1/3 +1/2 . 2/3`
`= 1/2. (1/3+2/3)`
`= 1/2. 3/3`
`=1/2 .1`
`=1/2`
`d, 3/2 - 1/3 +2/5`
`= 45/30 - 10/30 + 12/30`
`=(45-10+12)/30`
`= 47/30`
= 7( 5/14 + 4/77 + 3/154 + 1/210 + 13/420)
= 7(5/2.7 + 4/7.11 + 3/11.14 + 1/14.15 + 13/15.28)
= 7( 1/2 - 1/7 + 1/7 - 1/11 +.....+ 1/15 - 1/28)
= 7( 1/2 - 1/28)
= 7 . 13/28
= 13/4