tính A=1+1/3+1/6+1/10+1/15+...+1/120
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LV
0
LQ
1
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
20 tháng 12 2023
A = \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) +.. . + \(\dfrac{1}{120}\)
A = \(\dfrac{2}{2}\).(\(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + ... + \(\dfrac{1}{120}\))
A = 2.( \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) + ... + \(\dfrac{1}{240}\))
A = 2.( \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + ... + \(\dfrac{1}{15.16}\))
A =2 .( \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{15}\) - \(\dfrac{1}{16}\))
A = 2.( \(\dfrac{1}{2}\) - \(\dfrac{1}{16}\))
A = 2.\(\dfrac{7}{16}\)
A = \(\dfrac{7}{8}\)
KT
9 tháng 8 2018
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{105}+\frac{1}{210}\)
=> \(\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+.....+\frac{1}{210}+\frac{1}{240}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{14.15}+\frac{1}{15.16}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{!}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{16}\)
\(=\frac{1}{2}-\frac{1}{16}=\frac{7}{16}\)
=> \(A=\frac{7}{8}\)
US
0
MN
2
12 tháng 4 2016
A= 3.136.8+4.14.6- 14.150
= 24.136+24.16- 14.150
= 24. (136+14)- 14. 150
= 24. 150- 14.150
= 150. (24-14)=150. 10= 1500
5 tháng 4 2018
A= 24.136 + 24.14 - 14.150
= 24.(136 + 14)- 14.150
= 24.150 - 14.150
= 150. (24- 14)=150.10 =1500
S
16 tháng 7 2016
\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}\)
\(=\frac{6}{21}\)
2
8 tháng 5 2015
A=\(2.\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+......+\frac{1}{240}\right)\)
A=\(2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)
A=\(2.\left(\frac{1}{4.}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.......+\frac{1}{15}-\frac{1}{16}\right)\)
A=\(2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
A=\(2.\left(\frac{4}{16}-\frac{1}{16}\right)\)
\(A=2.\frac{3}{16}\)
\(A=\frac{3}{8}\)
\(Vay\) \(A=\frac{3}{8}\)