1+2+3+4...+2014=
Những câu hỏi liên quan
A=2014+[2014:(1+2)]+[2014:(1+2+3)]+[2014:(1+2+3+4)]+...++[2014:(1+2+3+...+2013)]
rut gon bieu thuc
1/(1^4+1^2+1)+2/(2^4+2^2+1)+3/(3^4+3^2+1)+...+2014/(2014^4+2014^2+2014)=...
{giup minh vs}
Rút gọn biểu thức : \(\frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+2}+\frac{3}{3^4+3^2+3}+...+\frac{2014}{2014^4+2014^2+2014}\)
Tính:
A= 2014 + \(\frac{2014}{1+2}+\frac{2014}{1+2+3}+\frac{2014}{1+2+3+4}+........+\frac{2014}{1+2+3+4+.....+2013}\)
\(A=2014.\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+2013}\right)\)
\(A=2014.\left(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1007.2013}\right)\)
\(A=2.2014.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2013.2014}\right)\)
\(A=2.2014.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\right)\)
\(A=2.2014.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}\right)\)
\(A=2.2014.\left(1-\frac{1}{2014}\right)\)
\(A=2.2014.\frac{2013}{2014}\)
\(A=\frac{2.2014.2013}{2014}\)
\(A=2.2013\)
\(A=4026\)
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1) 1/2 + 1/3 + 1/4 + ... + 1/2013 + 1/2014
2) 2014 + 2013/2 + 2012/3 + 2011/4 + ... + 2/2013 + 1/2014
1*2*3*4......2015-1*2*3*4...2014-1*2*3*4......2013*2014^2
\(1.2.3.4..............2015-1.2.3.4..............2014-1.2.3.4.........2013.2014^2\)
\(=1.2.3........2013.\left(2014.2015-2014-2014^2\right)\)
\(=1.2.3..........2013.\left[2014.\left(2015-1-2014\right)\right]\)
\(=1.2.3............2013.\left(2014.0\right)\)
\(=1.2.3.........2013.0\)
=0
Chúc bn học tốt
1*2*3*4......2015-1*2*3*4...2014-1*2*3*4......2013*2014^2
Rút gọn biểu thức: \(\frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+1}+\frac{3}{3^4+3^2+1}+...+\frac{2014}{2014^4+2014^2+1}\)
Tính tổng:
A= 1+2014^1+2014^2+2014^3+...+2014^2014+2014^2015
B = 3-3^2+3^3+3^4+...+3^100
A = 1 + 2014^1 + 2014^2 + 2014^3 + ... + 2014^2014 + 2014^2015
2014A = 2014^1 + 2014^2 + 2014^3 + 2014^4 + ... 2014^2015 + 2014^2016
2014A - A = ( 2014^1 + 2014^2 + 2014^3 + 2014^4 + .... + 2014^2015 + 2014^2016 ) - ( 1 + 2014^1 + 2014^2 + 2014^3 + ... + 2014^2014 + 2014^2015 )
2013A = 2014^2016 - 1
A = 2014^2016 - 1 / 2013
B = 3 - 3^2 + 3^3 + 3^4 + ... + 3^100 ( đề hơi vui )
3B = 3^2 - 3^3 + 3^4 + 3^5 + ... + 3^101
3B - B = ( 3^2 - 3^3 + 3^4 + 3^5 + ... + 3^101 ) - ( 3 - 3^2 + 3^3 + 3^4 + ... + 3^100 )
2B = ( 3^2 - 3^3 + 3^4 + 3^5 + ... + 3^101 ) - 3 + 3^2 - 3^3 - 3^4 - ... - 3^100
2B = 3^2 - 3^3 + 3^101 - 3 + 3^2 - 3^3
2B = 9 - 27 + 3^101 - 3 + 9 - 27
2B = -18 + 3^101 - 3 + ( -18 )
2B = -39 + 3^101
B = -39 + 3^101 / 2
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A = 1 + 2014 + 20142 + 20143 + ... + 20142014 + 20142015
2014A = 2014 + 20142 + 20143 + 20144 + ... + 20142015 + 20142016
2014A - A = ( 2014 + 20142 + 20143 + 20144 + ... + 20142015 + 20142016 ) - ( 1 + 2014 + 20142 + 20143 + ... + 20142014 + 20142015 )
2013A = 20142016 - 1
A \(=\frac{2014^{2016}-1}{2013}\)
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B = 3 - 32 + 33 - 34 + ... + 3100
3B= 32 - 33 + 34 - 35 + ... + 3101
3B + B = ( 3 - 32 + 33 - 34 + ... + 3100 ) + ( 32 - 33 + 34 - 35 + ... + 3101 )
4B = 3 + 3101
B = \(\frac{3+3^{101}}{4}\)
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2014+(2014/1+2)+(2014/1+2+3)+...+(2014/1+2+3+4+5+...+2013)=???.Ai giai duoc vay???
2014+(2014/1+2)+(2014/1+2+3)+...+(2014/1+2+3+...+2013)
=2014*(1+(1/1+2)+(1/1+2+3)+...+( 1/1+2+3+...+2013))
=2014*(1+(1/3)+(1/6)+....+(1/2027091)
=2014*2*((1/+(1/2*3)+(1/3*4).....+(1/2013*2014))
=2014*2*(1/1-1/2+1/2-1/3+1/3-1/4+.....+1/2013-1/2014)
=2014*2*(1-1/2014)
=2*(2014*2013/2014)
=2*2013
=4026
Cuối cùng cũng giải được.
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