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LH
1
YN
2 tháng 2 2023
\(P=\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)...\left(1-\dfrac{1}{1225}\right)\left(1-\dfrac{1}{1275}\right)\)
\(=\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}...\dfrac{1224}{1225}.\dfrac{1274}{1275}\)
\(=\dfrac{2.2}{3.2}.\dfrac{5.2}{6.2}.\dfrac{9.2}{10.2}...\dfrac{1224.2}{1225.2}.\dfrac{1274.2}{1275.2}\)
\(=\dfrac{4}{9}.\dfrac{10}{12}.\dfrac{18}{20}...\dfrac{2448}{2450}.\dfrac{2548}{2550}\)
\(=\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}...\dfrac{48.51}{49.50}.\dfrac{49.52}{50.51}\)
\(=\dfrac{1.2.3...48.49}{2.3.4...49.50}.\dfrac{4.5.6...51.52}{3.4.5...50.51}\)
\(=\dfrac{1}{50}.\dfrac{52}{3}\)
\(=\dfrac{26}{75}\).
ND
0
MA
1
H
5 tháng 4 2021
\(P=\left(1-\dfrac{1}{3}\right)+\left(1-\dfrac{1}{6}\right)+...+\left(1-\dfrac{1}{1225}\right)+\left(1-\dfrac{1}{1275}\right)\\ \Rightarrow\dfrac{P}{2}=\left(\dfrac{1}{2}-\dfrac{1}{6}\right)+\left(\dfrac{1}{2}-\dfrac{1}{12}\right)+...+\left(\dfrac{1}{2}-\dfrac{1}{2550}\right)\\ =\left(\dfrac{1}{2}-\dfrac{1}{2\cdot3}\right)+\left(\dfrac{1}{2}-\dfrac{1}{3\cdot4}\right)+...+\left(\dfrac{1}{2}-\dfrac{1}{50\cdot51}\right)\\ =\dfrac{1}{2}\cdot49-\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{50\cdot51}\right)\\ =\dfrac{49}{2}-\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{50}-\dfrac{1}{51}\right)\\ =\dfrac{49}{2}-\dfrac{1}{2}+\dfrac{1}{51}=\dfrac{1225}{51}\\ \Rightarrow P=\dfrac{2450}{51}\)
27 tháng 3 2017
2xC=2+6+12+20+...+2450
2xC=1x2+2x3+3x4+4x5+...+49x50
6xC=1x2x3+2x3x3+3x4x3+...+49x50x3
6xC=1x2x3+2x3x(4-1)+3x4x(5-2)+...+49x50x(51-48)
6xC=1x2x3+2x3x4-1x2x3+....+49x50x51-48x49x50
6xC=49x50x51
6xC=124950
C=20825
k nhé đúng 100%
14 tháng 1 2023
2C = 2+6+12+20+30+...+2450
2C = 1.2+2.3+3.4+4.5+5.6+...+49.50
3C = 1.2.3+2.3.3+3.4.3+4.5.3+5.6.3+...+49.50.3
3C = 1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+5.6.(7-4)+...+49.50.(51-48)
3C = 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+5.6.7-4.5.6+5.6.7-4.5.6+....+49.50.51-48.49.50
=>C=49.50.51 : 3 =>C=4650
PQ
1
13 tháng 7 2016
A = -1 - 1/3 - 1/6 - 1/10 - 1/15 - ... - 1/1225
A = -(1 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/1225)
A = -(2/2 + 2/6 + 2/12 + 2/20 + 2/30 + ... + 2/2450)
A = -2.(1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/49.50)
A = -2.(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/49 - 1/50)
A = -2.(1 - 1/50)
A = -2.49/50
A = -49/25
NV
A= (1/3-1).(1/6-1).(1/10-1).(1/15-1)....(1/1225-1).(1/1275-1)
B=2^19.27^3-15.4^9.9^4 / 6^9.2^10-12^10
0
VT
4
17 tháng 9 2016
1) 1 + 2 + 3 + ... + x = 1225
=> (1 + x).x:2 = 1225
=> (1 + x).x = 1225.2
=> (1 + x).x = 2450
=> (1 + x).x = 50.49 = (-49).(-50)
Vậy \(x\in\left\{50;-49\right\}\)
2) 2 + 4 + 6 + ... + 2x = 210
=> 2.(1 + 2 + 3 + ... + x) = 210
=> 2.(1 + x).x:2 = 210
=> (1 + x).x = 15.14 = (-14).(-15)
Vậy \(x\in\left\{15;-14\right\}\)
IM
17 tháng 9 2016
a)
\(1+2+......+x=1225\)
\(\Rightarrow\frac{\left(x+1\right)x}{2}=1225\)
\(\Rightarrow\left(x+1\right)x=2450\)
\(\Rightarrow\left(x+1\right)x=49.50\)
=> x = 49
Vậy x = 49
b)
\(2+4+....+2x=210\)
\(\Rightarrow2\left(1+2+....+x\right)=210\)
\(\Rightarrow2.\frac{\left(x+1\right)x}{2}=210\)
\(\Rightarrow x\left(x+1\right)=210\)
\(\Rightarrow x\left(x+1\right)=210\)
\(\Rightarrow x\left(x+1\right)=14.15\)
=> x = 14
Vậy x = 14