Tính A=1/3+1/6+1/10+1/15+......+1/190
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=2*(1/6+1/12+1/20+...+1/380)
=2*(1/2*3+1/3*4+1/4*5+...+1/19*20)
=2*(1/2-1/3+1/3-1/4+1/4-1/5+...+1/19-1/20)
=2*(1/2-1/20)
=2*(10/20-1/20)
=2*9/20
=18/20
=9/10
\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\left|\frac{-3}{10}+\frac{1}{2}\right|-\frac{1}{6}\)
\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\frac{1}{5}-\frac{1}{6}\)
\(\frac{4}{3}-\left(x-\frac{1}{5}\right)=\frac{1}{30}\)
\(x-\frac{1}{5}=\frac{4}{3}-\frac{1}{30}\)
\(x-\frac{1}{5}=\frac{13}{10}\)
\(x=\frac{13}{10}+\frac{1}{5}\)
\(x=\frac{3}{2}\)
\(A=\left(a\text{x}7+a\text{x}8-a\text{x}15\right):\left(1+2+3+...+10\right)\)
\(A=\left(a\text{x}\left(7+8-15\right)\right):\left(1+2+3+...+10\right)\)
\(A=\left(a\text{x}0\right):\left(1+2+3+..+10\right)\)
\(A=0:\left(1+2+3+...+10\right)\)
\(A=0\)
\(B=\left(18-9\text{x}2\right)\text{x}\left(2+4+6+8+10\right)\)
\(B=\left(18-18\right)\text{x}\left(2+4+6+8+10\right)\)
\(B=0\text{x}\left(2+4+6+8+10\right)\)
\(B=0\)
a) 1/7 . 5/6 + 1/7 . 1/6 + -8/7
= 1/7 . ( 5/6 + 1/6 ) + -8/7
= 1/7 . 1 + -8/7
= 1/7 + -8/7 = -1
b) 3/5 . -4/9 . 5/3 . 18/7
= ( 3/5 . 5/3 ) . ( -4/9 . 18/7 )
= 1 . -8/7 = -8/7
c) 1/2 + -3/4 . 16/9
= 1/2 + -4/3 = -5/6
d) ( 1/7 + 5/14 ) . -28/3
= 1/2 . -28/3 = -14/3
Tổng trên có 2016 số hạng nên tổng trên là:
(2016+1)x2016:2=2033136
Cách 1 : \(\left(\frac{1}{4}-\frac{1}{7}\right)\times\frac{1}{3}\)
\(=\frac{3}{28}\times\frac{1}{3}\)
\(=\frac{1}{28}\)
Cách 2:\(\left(\frac{1}{4}-\frac{1}{7}\right)\times\frac{1}{3}\)
\(=\frac{1}{4}\times\frac{1}{3}-\frac{1}{7}\times\frac{1}{3}\)
\(=\frac{1}{12}-\frac{1}{21}\)
\(=\frac{1}{28}\)
7/13
\(A=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{190}\)
\(=\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{380}\)
\(=2\left(\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{380}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{19}-\dfrac{1}{20}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{20}\right)=2\cdot\dfrac{9}{20}=\dfrac{9}{10}\)