tính nhanh:
-1 2010 :20100 +15 : (-3)
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A = (30: 7\(\dfrac{1}{2}\)) : (\(\dfrac{1}{15}\):0,5) -1,5\(\times\)(4\(\dfrac{1}{2}\)-\(\dfrac{9}{2}\))
A = (30 : \(\dfrac{15}{2}\)): (\(\dfrac{1}{15}\) \(\times\) 2) - 1,5 \(\times\) (\(\dfrac{9}{2}\) - \(\dfrac{9}{2}\))
A = (30 \(\times\) \(\dfrac{2}{15}\)) : \(\dfrac{2}{15}\) - 1,5 \(\times\) 0
A = 4 \(\times\) \(\dfrac{15}{2}\) - 0
A = 30
Ta có:
$S=\dfrac{5}{1\cdot2\cdot3}+\dfrac{8}{2\cdot3\cdot4}+\dfrac{11}{3\cdot4\cdot5}+\cdots+\dfrac{6026}{2008\cdot2009\cdot2010}$
Nhận thấy tử số có dạng $3n+2$, nên:
$S=\sum_{n=1}^{2008}\dfrac{3n+2}{n(n+1)(n+2)}$
Ta có: $\dfrac{3n+2}{n(n+1)(n+2)}=\dfrac{1}{n(n+1)}+\dfrac{2}{(n+1)(n+2)}$
Do đó:
$S=\left(\dfrac1{1\cdot2}+\dfrac1{2\cdot3}+\cdots+\dfrac1{2008\cdot2009}\right)$
$+2\left(\dfrac1{2\cdot3}+\dfrac1{3\cdot4}+\cdots+\dfrac1{2009\cdot2010}\right)$
Mà: $\dfrac1{n(n+1)}=\dfrac1n-\dfrac1{n+1}$
Nên: $S=\left(1-\dfrac1{2009}\right)+2\left(\dfrac12-\dfrac1{2010}\right)$
$=1-\dfrac1{2009}+1-\dfrac1{1005}$
$=2-\dfrac1{2009}-\dfrac1{1005}$
Vì: $\dfrac1{2009}+\dfrac1{1005}>0$
Nên $S<2$
\(=\dfrac{3}{2}-\dfrac{2}{21}-\dfrac{7}{12}+\left[\dfrac{15}{21}-\dfrac{1}{3}+\dfrac{5}{4}-\dfrac{2}{7}-\dfrac{1}{3}\right]\)
=11/12-2/21+5/7-2/3+5/4-2/7
=11/12-2/3+5/4-2/21+3/7
=11/12-8/12+15/12-2/21+9/21
=18/12+7/21
=3/2+1/3
=9/6+2/6=11/6
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(\dfrac{1}{3}-\dfrac{5}{4}\right)-\left(\dfrac{2}{7}+\dfrac{1}{3}\right)\right]\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(-\dfrac{11}{12}\right)-\dfrac{13}{21}\right]\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\dfrac{85}{84}\right\}\)
\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left(-\dfrac{3}{7}\right)\)
\(B=\dfrac{11}{6}\)
\(=\left(1+3+...+2021\right)\cdot\left[1001\cdot135\cdot137-1001\cdot135\cdot137\right]\)
\(=\left(1+3+...+2021\right)\cdot0\)
=0
= (1 + 3 + ... + 2021) x (135 x 1001 x 137 - 135 x 137 x 1001)
= (1 + 3 + ... + 2021) x 0
= 0
1.
-15 - 12 = -15 + (-12) = -27
0+ (-7)= 0-7 = -7
0-(-5) = 0 + 5 = 5
đap số 1 . - 27
2. -7
3. 5
Số số hạng là :
( 50 - 5 ) : 5 + 1 = 10 ( số )
Tổng trên là :
( 50 + 5 ) . 10 : 2 = 275
Vậy,.............
\(-1^{2010}\): \(2010^0\) \(+\)\(15\)\(\div\)\((-3)\)
=\(1\) \(\div\) \(1\) \(+\) \(15\) \(\div\) \((-3)\)
=\(1\) \(+\) \((-5)\)
=\((-4)\)