tinh 1/60+1/100+1/150+1/210+..+1/660
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
XO
13 tháng 7 2019
\(\frac{1}{10}+\frac{1}{30}+\frac{1}{60}+\frac{1}{100}+\frac{1}{150}\)
= \(\frac{1}{10}.\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right)\)
= \(\frac{1}{10}.2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)
= \(\frac{1}{5}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
= \(\frac{1}{5}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
= \(\frac{1}{5}.\left(1-\frac{1}{6}\right)\)
= \(\frac{1}{5}.\frac{5}{6}\)
= \(\frac{1}{6}\)
13 tháng 7 2019
\(\frac{1}{10}+\frac{1}{30}+\frac{1}{60}+\frac{1}{100}+\frac{1}{150}\)
\(=\frac{1}{10}.\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right)\)
\(=\frac{1}{10}.2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)
\(=\frac{1}{10}.2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
\(=\frac{1}{10}.2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
\(=\frac{1}{5}.\left(1-\frac{1}{6}\right)\)
\(=\frac{1}{5}.\frac{5}{6}\)
\(=\frac{1}{6}\)
Rất vui vì giúp đc bạn <3
BN
30 tháng 12 2017
A = \(\frac{2}{3}\). \(\frac{5}{6}\). \(\frac{9}{10}\).\(\frac{14}{15}\)... \(\frac{209}{210}\)
= \(\frac{4}{6}\). \(\frac{10}{12}\).\(\frac{18}{20}\).\(\frac{28}{30}\)... \(\frac{418}{420}\)
= \(\frac{4.10.18.28...418}{6.12.20.30...420}\)
= \(\frac{1.4.2.5.3.6.4.7...19.22}{2.3.3.4.4.5.5.6...20.21}\)
= \(\frac{\left(1.2.3.4...19\right)\left(4.5.6.7...22\right)}{\left(2.3.4.5...20\right)\left(3.4.5.6...21\right)}\)
= \(\frac{1.22}{20.3}\)= \(\frac{22}{60}\)= \(\frac{11}{30}\)
CM
14 tháng 7 2017
=14\15.20\21....209\210
=14.2\15.2.20.2\21.2....209.2\210.2
=4.7\5.6.5.8\6.7.....19.20\20.21
=4.5.6....19\5.6.7...20.7.8.9....22\6.7.8.....21
=4\20.22\6
=1\5-11\3
=11\15
k cho mik nha
17 tháng 1 2016
\(S=1+\frac{1}{2}+\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{101}{2}\)
\(S=1+\frac{1+2+3+4+...+101}{2}\)
\(S=1+\frac{10201}{2}=...\)
tick cho mink nha!
30 tháng 6 2016
Ta có:\(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{210}\)
\(=\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+....+\frac{1}{14.15}\)
\(=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{15}\)
\(=\frac{1}{6}-\frac{1}{15}=\frac{1}{10}\)
TB
2
19 tháng 8 2015
gọi biểu thức tên là A , ta có :
A= (1/21+1/210+1/2010). ( 1/3-1/30-1/5-1/10)
A = (1/21+1/210+1/2010) . 0
A = 0