2/2.4.6+2/4.6.8+...+2/38.40.42
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NL
2
8 tháng 5 2018
\(A=\frac{2}{2.4.6}+\frac{2}{4.6.8}+\frac{2}{6.8.10}+\frac{2}{8.10.12}\)
\(A=\frac{2}{48}+\frac{2}{192}+\frac{2}{480}+\frac{2}{960}\)
\(A=\frac{1}{24}+\frac{1}{96}+\frac{1}{240}+\frac{1}{480}\)
\(A=\frac{20}{480}+\frac{5}{480}+\frac{2}{480}+\frac{1}{480}\)
\(A=\frac{7}{120}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
14 tháng 3
A = \(\dfrac{2}{2.4.6}\) + \(\dfrac{2}{4.6.8}\) + \(\dfrac{2}{6.8.10}\) + \(\dfrac{2}{8.10.12}\)
A = \(\dfrac{2}{2}\).(\(\dfrac{2}{2.4.6}\) + \(\dfrac{2}{4.6.8}\) + \(\dfrac{2}{6.8.10}\) + \(\dfrac{2}{8.10.12}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{2.2}{2.4.6}\) + \(\dfrac{2.2}{4.6.8}\) + \(\dfrac{2.2}{6.8.10}+\dfrac{2.2}{8.10.12}\))
A = \(\dfrac{1}{2}\).( \(\dfrac{4}{2.4.6}+\dfrac{4}{4.6.8}+\dfrac{4}{6.8.10}+\dfrac{4}{8.10.12}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{1}{2.4}\) - \(\dfrac{1}{4.6}\) +\(\dfrac{1}{4.6}\) - \(\dfrac{1}{6.8}\) + \(\dfrac{1}{6.8}\) - \(\dfrac{1}{8.10}\) + \(\dfrac{1}{8.10}\) - \(\dfrac{1}{10.12}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{1}{2.4}\) - \(\dfrac{1}{10.12}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{1}{8}-\dfrac{1}{120}\))
A = \(\dfrac{1}{2}\).\(\dfrac{7}{60}\)
A = \(\dfrac{7}{120}\)
HN
3
MH
19 tháng 2 2016
S = 2.4.6 + 4.6.8 + ... + 98.100.102
=> 8S = 2.4.6.8 + 4.6.8.8 + ... + 98.100.102.8
=> 8S = 2.4.6.(8 - 0) + 4.6.8.(10 - 2) + ... + 98.100.102.(104 - 96)
=> 8S = 2.4.6.8 - 0 + 4.6.8.10 - 2.4.6.8 + ... + 98.100.102.104 - 96.98.100.102
=> 8S = 98.100.102.104
=> S = 98.100.102.104/8
=> S = 12994800
19 tháng 2 2016
=> 8S = 2.4.6.8 + 4.6.8.8 + 6.8.10.8 + .... + 98.100.102.8
=> 8S = 2.4.6.8 + 4.6.8.( 10 - 2 ) + 6.8.10.( 12 - 4 ) + .... + 98.100.102.( 104 - 96 )
=> 8S = 2.4.6.8 + 4.6.8.10 - 2.4.6.8 + 6.8.10.12 - 4.6.8.10 + .... + 98.100.102.104 - 96.98.100.102
=> 8S = ( 2.4.6.8 - 2.4.6.8 ) + ( 4.6.8.10 - 4.6.8.10 ) + .... + ( 96.98.100.102 - 96.98.100.102 ) + 98.100.102.104
=> 8S = 98.100.102.104
=> S = \(\frac{98.100.102.104}{8}\)
29 tháng 3 2016
Ta có :
B = 2 . 4 . 6 + 4 . 6 .8 + ......+ 96 .98 .100
B.8 = 2 . 4 . 6 . 8 + 4. 6 . 8 .( 1 0 - 2) +........+96 . 98 . 100 . ( 102 - 94 )
8B = 2 . 4 . 6 .8 + 4. 6 .8 . 10 - 2 . 4 . 6 . 8 +......+ 96 . 98 . 100. 102 - 94 . 96 . 98 . 100
8B = 96 . 98 . 100 . 102
B = 96 . 98 . 100 .1 02 : 8
B = 12 . 98 . 100. 102
NT
0
NP
0
TG
0
Olm chào em. Đây là dạng toán nâng cao chuyên đề tính nhanh tổng các phân số quy luật. Cấu trúc thi chuyên, thi hsg. Hôm nay, Olm.vn sẽ hướng dẫn các em làm dạng này như sau:
Giải
A = \(\dfrac{2}{2.4.6}\) + \(\dfrac{2}{4.6.8}\) + ... + \(\dfrac{2}{38.40.42}\)
A = \(\dfrac{2}{2}\).(\(\dfrac{2}{2.4.6}+\dfrac{2}{4.6.8}+...+\dfrac{2}{38.40.42}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{2.2}{2.4.6}+\dfrac{2.2}{4.6.8}+\dfrac{2.2}{38.40.42}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{4}{2.4.6}+\dfrac{4}{4.6.8}+...+\dfrac{4}{38.40.42}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{1}{2.4}\) - \(\dfrac{1}{4.6}\) + \(\dfrac{1}{4.6}\) - \(\dfrac{1}{6.8}\)+ ... + \(\dfrac{1}{38.40}\) - \(\dfrac{1}{40.42}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{1}{2.4}\) - \(\dfrac{1}{40.42}\))
A = \(\dfrac{1}{2}\).(\(\dfrac{1}{8}\) - \(\dfrac{1}{1680}\))
A = \(\dfrac{1}{2}\).\(\dfrac{209}{1680}\)
A = \(\dfrac{209}{3360}\)