tính tổng A=1/30+1/42+1/56+1/72+...+1/380
K
Khách
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AA
1
MH
2 tháng 2 2021
\(A=-\dfrac{1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\\ A=-\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\\ A=-\left(\dfrac{5-4}{4.5}+\dfrac{6-5}{5.6}+\dfrac{7-6}{6.7}+\dfrac{8-7}{7.8}+\dfrac{9-8}{8.9}+\dfrac{10-9}{9.10}\right)\\ A=-\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ A=-\left(\dfrac{1}{4}-\dfrac{1}{10}\right)=-\dfrac{3}{20}.\)
29 tháng 6 2023
Sửa đề: A=-1/20+(-1/30)+(-1/42)+(-1/56)+(-1/72)+(-1/90)
=-(1/20+1/30+...+1/90)
=-(1/4-1/5+1/5-1/6+...+1/9-1/10)
=-1/4+1/10
=-5/20+2/20=-3/20
DT
0
PT
1
YN
30 tháng 3 2022
`Answer:`
\(A=-\frac{1}{20}+-\frac{1}{30}+-\frac{1}{42}+-\frac{1}{56}+-\frac{1}{72}+-\frac{1}{90}\)
\(=-\frac{1}{20}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}-\frac{1}{72}-\frac{1}{90}\)
\(=-\frac{1}{20}-\left(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(=-\frac{1}{20}-\left(\frac{1}{5}-\frac{1}{10}\right)\)
\(=-\frac{1}{20}-\frac{1}{10}\)
\(=-\frac{3}{20}\)
PN
12
3 tháng 1 2016
A=1/20+1/30+1/42+1/56+1/72+1/90
A=1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10
A=1/4-1/5+1/5-1/6+...+1/9-1/10
A=1/4-1/10
A=3/20
V
1
Q
19 tháng 4 2023
A=\(\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\)
A=\(-\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\)
A=\(-\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
A=\(-\left(\dfrac{1}{4}-\dfrac{1}{10}\right)\)
A=\(-\dfrac{3}{20}\)
tách đc như bước 3 là nhờ công thức \(\dfrac{1}{n\left(n+1\right)}=\dfrac{1}{n}-\dfrac{1}{n+1}\) hoặc \(\dfrac{k}{n\left(n+k\right)}=\dfrac{1}{n}-\dfrac{1}{n+k}\) nhé
K
4
O
8 tháng 4 2022
\(A=\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\)
\(A=\dfrac{-1}{4\cdot5}+\dfrac{-1}{5\cdot6}+\dfrac{-1}{6\cdot7}+\dfrac{-1}{7\cdot8}+\dfrac{-1}{8\cdot9}+\dfrac{-1}{9\cdot10}\)
\(A=\dfrac{-1}{4}-\dfrac{-1}{5}+\dfrac{-1}{5}-\dfrac{-1}{6}+\dfrac{-1}{6}-\dfrac{-1}{7}+\dfrac{-1}{7}-\dfrac{-1}{8}+\dfrac{-1}{8}-\dfrac{-1}{9}+\dfrac{-1}{9}-\dfrac{-1}{10}\)
\(A=\dfrac{-1}{4}-\dfrac{-1}{10}\)
\(A=-\dfrac{3}{20}\)
TH
2
T1
1 tháng 4 2018
\(=-1\left(\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}\right)\)
\(=-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=-\left(\frac{1}{4}-\frac{1}{10}\right)\)
\(=-\frac{3}{20}\)
BT
0
\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{380}=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{19.20}\)
=> \(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{5}-\frac{1}{20}\)
=> \(A=\frac{3}{20}\)
A = 1/30 + 1/42 + 1/56 + 1/72 +....+ 1/380
A = 1/5x6 + 1/6x7 + 1/7x8 + 1/8x9 +.....+1/19x20
A = 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 +......+ 1/19 - 1/20
A = 1/5 - 1/20 = 3/20