1/3+1/6+1/10+.....+1/45
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Tính nhanh:
a/ (1*5*6+2*10*12+4*20*24+9*45*54)/(1*3*5+2*6*10+4*12*20+9*27*45)
b/ [(1*5*6)+(2*10*12)+(4*20*24)+(9*45*54)]/[(1*3*5)+(2*6*10)+(4*12*20)+(9*27*45)]
/ là phân số nha!!!!!!!!!!!!!
23 tháng 3 2022 lúc 19:56
1+1+1+1+1+2+3+4+5+6+7+8+9+10 x 1+1+1+1+1+2+3+4+5+6+7+8+9+10 +1+1+1+1+1+2+3+4+5+6+7+8+9+10 - 10 x 9 - 9 + 45 +46 +47 =
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E= (1/3-1).(1/6-1).(1/10-1)...(1/45-1)
\(E=\left(\dfrac{1}{3}-1\right)\cdot\left(\dfrac{1}{6}-1\right)\cdot\left(\dfrac{1}{10}-1\right)\cdot...\cdot\left(\dfrac{1}{45}-1\right)\)
\(E=1\cdot\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{45}\right)\)
\(E=1\cdot\left(\dfrac{1}{45}-\dfrac{1}{3}\right)\div2+1\)
\(E=\dfrac{1}{22}\)
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E= (1/3-1).(1/6-1).(1/10-1)...(1/45-1)
\(E=\left(\dfrac{1}{3}-1\right)\cdot\left(\dfrac{1}{6}-1\right)\cdot\left(\dfrac{1}{10}-1\right)\cdot...\cdot\left(\dfrac{1}{45}-1\right)\)
\(\text{E=}\left(\dfrac{1}{3+6+10+...+45}\cdot1\right)\)
\(\text{E = }\left(\dfrac{1}{\left(45-3\right)\div2+1}\right)\)
\(\text{E = }\dfrac{1}{22}\)
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s=1+1/3+1/6 +1/10................+1/45 =?
\(S=1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{45}\)
\(S=2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)\)
\(S=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
\(S=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(S=2.\left(1-\frac{1}{10}\right)\)
\(S=2.\frac{9}{10}\)
\(S=\frac{9}{5}\)
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B=1/3+1/6+1/10+1/15+....+1/45
A= 1/3+1/6+1/10+1/15=....+1/45
Nhân cả tử cả mẫu của các phân số trong A với 2 ta có:
\(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+..........+\frac{2}{90}\)
\(=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.........+\frac{1}{90}\right)\)
\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+........+\frac{1}{9.10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+......+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=2.\frac{2}{5}\)
\(=\frac{4}{5}\)
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\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(A=\frac{2}{5}\)
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1/3 + 1/6 + 1/10 + 1/15 + ......+ 1/45
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{45}\)
\(=2\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}\right)\)
\(=2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\right)\)
\(=2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2\times\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=\frac{4}{5}\)
1) 1/1+2 + 1/1+2+3+.........+1/1+2+3+..............+10
2) 1+3+6+10+.........+45+55/1x10+2x9+.......+9x2+10x1