1/3 + 1/6 + 1/ 10 + .... + 1/300
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S1/2=1/2+1/6+1/12+...+1/600
S1/2=1/1*2+1/2*3+....+1/24*25
S1/2=1-1/25
S1/2=24/25
S=48/25
A= 1/3+1/6+...+1/300
1/2 x A = 1/2 x (1/3+1/6+...+1/300)
A/2 = 1/6+1/12+..+1/600
A/2 = 1/(2x3) + 1/(3x4) +....+ 1/ (24x25)
A/2 = 1/2-1/3+1/3-1/4+....+1/24-1/25
A/2 = 1/2 - 1/25
A/2 = 23/50
A = 23/25
vậy...
\(S=\frac{1}{3}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{300}\)
\(\Rightarrow\frac{1}{2}S=\frac{1}{6}+\frac{1}{12}+\cdot\cdot\cdot+\frac{1}{600}\)
\(\Rightarrow\frac{1}{2}S=\frac{1}{2\times3}+\frac{1}{3\times4}+\cdot\cdot\cdot+\frac{1}{24\times25}\)
\(\Rightarrow\frac{1}{2}S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdot\cdot\cdot+\frac{1}{24}-\frac{1}{25}\)
\(\Rightarrow\frac{1}{2}S=\frac{1}{2}-\frac{1}{25}\)
\(\Rightarrow\frac{1}{2}S=\frac{23}{50}\)
\(\Rightarrow S=\frac{23}{50}:\frac{1}{2}\)
\(\Rightarrow S=\frac{23}{25}\)
S = \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{300}\)
= \(2\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{600}\right)\)
= \(2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{24\times25}\right)\)
= \(2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{24}-\frac{1}{25}\right)\)
= \(2\times\left(\frac{1}{2}-\frac{1}{25}\right)\)
\(=2\times\frac{23}{50}\)
\(=\frac{23}{25}\)
1+2-3-4+5+6-7-8+9+9+10-11-12+12+...229-300+301+302
=(302+1)-(301+2)-(300+3)+(299+4)-...
=303-303-303-303-....
=0-0-0-0-0-....
=0
1+2-3-4+5+6-7-8+9+10-11-12+...-229-300+301+302
= (1+2-3)+(4+5+6-7)+...+(228-229-300+301)+302
= 0 + 0 +...+ 0 + 302
= 302
Ta chia thành: 1 + (2-3-4+5) + (6-7-8+9)+....+(298-299-300+301) + 302 = 1 + 0 + 0 + 0 + .....+ 0 + 302 = 1+302 = 303
1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 +........- 299 -300 + 301 +302
Theo đề ta có:
Cho A= 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 +........- 299 -300 + 301 +302
=> 1 + (2 - 3 - 4 + 5 )+ (6 - 7 - 8 + 9) + (10 - 11 - 12 +13)........(289- 299 -300 + 301) +302
=> 1+ 0+ 0+.....+ 0+ 302
=> 1+302
=> 303
Ta chia thành: 1 + (2-3-4+5) + (6-7-8+9)+....+(298-299-300+301) + 302 = 1 + 0 + 0 + 0 + .....+ 0 + 302 = 1+302 = 303
**** cho mk nha bạn !!!
\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{300}\)
\(=2.\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{24.25}\right)\)
\(=2.\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{24}-\dfrac{1}{25}\right)\)
\(=2.\left(\dfrac{1}{2}-\dfrac{1}{25}\right)\)
\(=\dfrac{23}{25}\)
cảm ơn bn yến nhi nha