Tính tổng A = 3 + ( -12 ) + 13 + ( - 33 ) +... + 93 + ( - 102 )
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Ta có :
3 + ( - 12 ) + 13 + ( -22 ) + ..........+ 93 + ( - 102 )
= [ 3 + ( -12 ) ] + [ 13 + ( -22 ) ] + ... + [ 93 + ( -102 ) ]
= -9 + ( -9 ) + .... + ( -9 )
= ( -9 ) . 10
= -90
\(a,\left(-5\right)+11+\left(-15\right)+21+\left(-25\right)+31+...+\left(-95\right)+101\\ =\left[\left(-5\right)+11\right]+\left[\left(-15\right)+21\right]+\left[\left(-25\right)+31\right]+...+\left[\left(-95\right)+101\right]\\ =6+6+6+...+6\left(10\text{ số }6\right)\\ =6\cdot10\\ =60\)
\(b,3+\left(-12\right)+13+\left(-22\right)+23+\left(-32\right)+...+93+\left(-102\right)\\ =\left[3+\left(-12\right)\right]+\left[13+\left(-22\right)\right]+\left[23+\left(-32\right)\right]+...+\left[93+\left(-102\right)\right]\\ =\left(-9\right)+\left(-9\right)+\left(-9\right)+...+\left(-9\right)\left(10\text{ số }-9\right)\\ =\left(-9\right)\cdot10\\ =-90\)
\(a,\left(-5\right)+11+\left(-15\right)+21+\left(-25\right)+31+...+\left(-95\right)+101\)
\(=\left[\left(-5\right)+11\right]+\left[\left(-15\right)+21\right]+\left[\left(-25\right)+31\right]+...+\left[\left(-95\right)+101\right]\)
\(=6+6+6+...+6\) (10 số 6)
\(=6.10=60\)
\(\)
a) Số các số hạng là:
(199 - 11) + 1 = 189 số
Tổng là:
189 x (199 + 11) : 2 = 19845
b) Số các số hạng là:
(99 - 1):2 + 1 = 50 số
Tổng là:
50 x (99 + 1):2 =2500
a, \(\dfrac{10}{17}\) + \(\dfrac{5}{-13}\) - \(\dfrac{11}{25}\) + \(\dfrac{7}{17}\) - \(\dfrac{8}{13}\)
= ( \(\dfrac{10}{17}\) + \(\dfrac{7}{17}\)) - ( \(\dfrac{5}{13}\) + \(\dfrac{8}{13}\)) - \(\dfrac{11}{25}\)
= \(\dfrac{17}{17}\) - \(\dfrac{13}{13}\) - \(\dfrac{11}{25}\)
= 1 - 1 - \(\dfrac{11}{25}\)
= - \(\dfrac{11}{25}\)
b, 0,3 - \(\dfrac{93}{7}\) - 70% - \(\dfrac{4}{7}\)
= 0,3 - 0,7 - ( \(\dfrac{93}{7}+\dfrac{4}{7}\))
= - 0,4 - \(\dfrac{97}{7}\)
= - \(\dfrac{2}{5}\) - \(\dfrac{97}{7}\)
= - \(\dfrac{499}{35}\)
a) \(100+98+96+...+2-97-95-93-...-3\)
= \(100+98+\left(96-97\right)+\left(94-95\right)+...+\left(2-3\right)\)
= \(100+98-95\) = \(103\)
b) \(2-4-6+8+10-12-14+16+...-102+104\)
= \(\left(2-4\right)+\left(-6+8\right)+\left(10-12\right)+\left(-14+16\right)+...+\left(-102+104\right)\)
= \(-2+2-2+2-2+...+2\) = \(0\)
c) \(1+2-3-4+5+6-7-8+9+10-11-12+...-111-112+113+114\)
= \(\left(1+2\right)-\left(3+4\right)+\left(5+6\right)-\left(7+8\right)+...\left(113+114\right)\)
= \(3-7+11-15+19-23+...+219-223+227\)
= \(\left(3-7\right)+\left(11-15\right)+\left(19-23\right)+...+\left(219-223\right)+227\)
= \(-4-4-4-4-...-4+227\)
= \(54\left(-4\right)+227\) = \(-216+227\) = \(11\)