Tính:5/6x9/5-5/6x4/5
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4/6x1/5+4/6x3/5+2/6x4/5
=4/6.(1/5+3/5)+2/6.4/5
=4/6.4/5+2/6.4/5
=4/5.(4/6+2/6)
=4/5.6/6
=4/5.1 = 4/5
Ta có 1/3x4= 1/3- 1/4
2/4x6= 1/4-1/6
..............................
5/13x18= 1/13 - 1/18
=> 1/3 -1/4 + 1/4 -1/6 +......+ 1/13 -1/18
= 1/3 - 1/18
= 5/18
tính vế trên trước: 2^12 x 3^5 - 4^6 x 9^2 = 4096 x 243 - 4096 x 81 = 4096 x ( 243 - 81 ) = 663552.
tính vế dưới sau : ( 2^2 x 3 )^6 + 8^4 x 3^5 = ( 4 x 3 )^6 + 4096 x 243 = 12^6 + 995328 = 2985984 + 995328 = 3981312.
Vậy được: 663552/3981312 = 1/6.
\(\dfrac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=\dfrac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\cdot\left(2\cdot3-1\right)}\)
\(=\dfrac{4}{5}\)
A = \(\dfrac{4}{3\times6}\) + \(\dfrac{4}{6\times9}\) + ......+ \(\dfrac{4}{18\times21}\)
A = \(\dfrac{4}{3}\) \(\times\) ( \(\dfrac{3}{3\times6}\) + \(\dfrac{3}{6\times9}\)+......+ \(\dfrac{3}{18\times21}\))
A = \(\dfrac{4}{3}\) \(\times\) ( \(\dfrac{1}{3}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{9}\)+.....\(\dfrac{1}{18}\) - \(\dfrac{1}{21}\))
A = \(\dfrac{4}{3}\) \(\times\) ( \(\dfrac{1}{3}\) - \(\dfrac{1}{21}\))
A = \(\dfrac{4}{3}\)\(\times\) \(\dfrac{2}{7}\)
A = \(\dfrac{8}{21}\)
\(P\left(x\right)=5^6-6.5^5+6.5^4-6.5^3+6.5^2-6.5+1=5^6-6\left(5^5-5^4-5^3-5^2-5\right)+1=1556\)
5/6x9/5-5/6x4/5
=5/6x(9/5-4/5)
=5/6x1
=5/6
\(\frac{5}{6}\times\frac{9}{5}-\frac{5}{6}\times\frac{4}{5}\)
\(=\frac{5}{6}\times\left(\frac{9}{5}-\frac{4}{5}\right)\)
\(=\frac{5}{6}\times1\)
\(=\frac{5}{6}\)