1/3+1/6+1/10+1/15+...+1/45
[giúp mk với ạ]
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M
2
5 tháng 9 2021
\(P=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}\)
\(=2\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\)
\(=2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{10}\right)=2.\dfrac{2}{5}=\dfrac{4}{5}\)
HS
3
CV
1 tháng 8 2017
Đặt A = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)
\(\frac{1}{2}A=\frac{1}{2}+\frac{1}{6}+\frac{1}{20}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(A=\frac{9}{10}.2\)
\(=\frac{9}{5}\)
1 tháng 8 2017
Đặt \(A=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}\)
=> \(\frac{1}{2}A=\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{45}\right).\frac{1}{2}\)
\(=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{9.10}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{10}\)
= \(1-\frac{1}{10}=\frac{9}{10}\)
=> A= 9/10:1/2=9/5
HT
3
19 tháng 1 2018
ta có
(1/3+1/6+1/36) +(1/10+1/15+1/45)+(1/21+1/28)
=(\(\frac{12+6+1}{36}\)+\(\frac{9+6+2}{90}\)+\(\frac{4+3}{84}\)
19/36+17/90+1/12
=(19/36+1/12)+17/90
=7/12+17/90
=105/180+34/180
=139/180
19 tháng 1 2018
1/3 +1/6+1/10+1/15+1/21+1/28+1/36+1/45
=1/1x3+1/3x2+1/2x5+1/3x5+1/3x7+1/7x4+1/4x9+1/9x5
=1/1-1/3+1/3-1/2....+1/9-1/5
=1/1
NX
17 tháng 8 2023
a) \(\dfrac{3}{8}+\dfrac{15}{-25}+\dfrac{3}{5}\)
\(=\dfrac{-9}{40}+\dfrac{3}{5}\)
\(=\dfrac{3}{8}\)
b) \(\dfrac{-5}{18}+\dfrac{23}{45}-\dfrac{9}{10}\)
\(=\dfrac{7}{30}-\dfrac{9}{10}\)
\(=\dfrac{-2}{3}\)
c) \(\dfrac{-5}{12}+\dfrac{15}{18}-2,25\)
\(=\dfrac{5}{12}-2,25\)
\(=\dfrac{-11}{6}\)
d) \(\dfrac{5}{6}+\dfrac{2}{3}-0,5\)
\(=\dfrac{3}{2}-0,5\)
\(=1\)
OY
20 tháng 7 2021
a) Đặt A= \(\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{36}\)
\(\dfrac{1}{2}\)A=\(\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\)
\(\dfrac{1}{2}\)A=\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}\)
\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{8}-\dfrac{1}{9}\)
\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{9}\)
\(\dfrac{1}{2}\)A=\(\dfrac{7}{18}\)
A=\(\dfrac{7}{9}\)
CC
4
12 tháng 4 2019
a (1/6 + 1/10 + 1/15) : (1/6 + 1/10 - 1/15)
= ( 5/30 + 3/30 + 2/30) : (5/30 + 3/30 - 2/30)
= 1/3 : 1/6 = 1/3 x 6/1 = 6/3 = 2
b (1/2 - 1/3 + 1/4 - 1/5) : (1/4 - 1/5)
= (1/2 - 1/3 + 1/4 - 1/5) : (1/4 - 1/5)
= 1/2 - 1/3 = 1/6
A = 1/3 + 1/6 +1/10 +1/15 +.....+1/45
A = 2/6 + 2/12+2/20+2/30 +.....+2/90
A = 2(\(\dfrac{1}{2.3}\)+ \(\dfrac{1}{3.4}\)+ \(\dfrac{1}{4.5}\)+\(\dfrac{1}{5.6}\)+.....+\(\dfrac{1}{9.10}\))
A = 2(1/2 -1/3 +1/3 -1/4 +1/4 -1/5 +1/5 -1/6 +....+1/9-1/10)
A =2(\(\dfrac{1}{2}\) - \(\dfrac{1}{10}\))
A = 2. \(\dfrac{2}{5}\)
A = 4/5
(dấu . là phép nhân)
13+16+110+115+...+14513+16+110+115+...+145
=2×(16+112+120+130+...+190)=2×(16+112+120+130+...+190)
=2×(12×3+13×4+14×5+...+19×10)=2×(12×3+13×4+14×5+...+19×10)
=2×(12−13+13−14+14−15+...+19−110)=2×(12−13+13−14+14−15+...+19−110)
=2×(12−110)=2×(12−110)
=45