thực hiện phép tính:
A=(157.57-99.57-572):57+57
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A=(157.57-99.57-572):57+57
A = 1 + 57
A = 58
B=1.2+2.3+3.4+............+n.(n+1)
B = 1.2+2.3+3.4+.............+n(n+1)
=1(1+1) + 2(2+1) + 3(3+1) +...+n(n+1)
=(1^2 + 2^2 + 3^2 +...+ n^2) + (1 + 2 + 3 + ...+ n)
ta có các công thức:
1^2 + 2^2 + 3^2 +...+ n^2 = n(n+1)(2n+1)/6
1 + 2 + 3 + ...+ n = n(n+1)/2
thay vào ta có:
S = n(n+1)(2n+1)/6 + n(n+1)/2
=n(n+1)/2[(2n+1)/3 + 1]
=n(n+1)(n+2)/3
\(A=\left(157.57-99.57-57^2\right):57+57\)
\(=\left[\left(157-99\right).57-57^2\right]:57+57\)
\(=\left[58.57-57^2\right]:57+57\)
\(=\left[3306-3249\right]:57+57\)
\(=57:57+57\)
\(=1+57=58\)
Vậy....
\(B=\left[160.\left(730-700\right):2^4-4^2\right].13\)
\(=\left[160.30:16-16\right].13\)
\(=\left[4800:16-16\right].13\)
\(=\left(300-16\right).13\)
\(=284.13=3692\)
Vậy...
\(C=\left(3^2.17+3^2.38-55\right):\left(2^3.68-2^3.13\right)\)
\(=\left(9.17+9.38-55\right):\left(8.68-8.13\right)\)
\(=\left[9.\left(17+38\right)-55\right]:\left[8.\left(68-13\right)\right]\)
\(=\left[9.55-55\right]:\left[8.55\right]\)
\(=\left[8.55\right]:\left[8.55\right]\)
\(=1\)
Vậy...
\(D=2.51^2:17^2+\left(8.5^2-2^4-3^2\right):56+2009\)
\(=2.8+\left(8.25-16-9\right):56+2009\)
\(=18+\left(200-16-9\right):56+2009\)
\(=18+175:56+2009\)
\(=18+\dfrac{25}{8}+2009\)
\(=\dfrac{16241}{8}\)
a: \(\left(-305\right)+400+305\)
\(=\left(-305+305\right)+400\)
=0+400
=400
b: \(\left(-511\right)-\left(-11\right)\)
=-511+11
=-(511-11)
=-500
c: \(0-\left(12345+15\right)\)
\(=0-12360\)
=-12360
d: \(333-\left[\left(-14657\right)+57\right]-78\)
\(=333+14657-57-78\)
\(=\left(333-78\right)+14600\)
\(=255+14600=14855\)
a: \(145+43+\left(-145\right)+57\)
\(=\left(145-145\right)+\left(43+57\right)\)
=0+100
=100
b: \(\left(-123\right)+101+\left(-777\right)+99\)
\(=\left(-123-777\right)+\left(101+99\right)\)
=-900+200
=-700
c: \(\left(-8955\right)+33+\left(-45\right)+\left(-133\right)\)
\(=\left(-8955-45\right)+\left(33-133\right)\)
\(=\left(-9000\right)+\left(-100\right)=-9100\)
d: \(\left(-2\right)+\left(-4\right)+\left(-6\right)+\left(-8\right)+\left(-10\right)+8+10+12\)
\(=\left(12-2\right)+\left(-4-6\right)+\left(-8+8\right)+\left(-10+10\right)\)
=10-10+0+0
=0
a) $371+731-271-531$
$=(371-271)+(731-531)$
$=100+200$
$=300$
b) $57+58+59+60+61-17-18-19-20-21$
$=(57-17)+(58-18)+(59-19)+(60-20)+(61-21)$
$=40+40+40+40+40$
$=40\cdot5$
$=200$
c) $9-10+11-12+13-14+15-16$
$=(9-10)+(11-12)+(13-14)+(15-16)$
$=-1+(-1)+(-1)+(-1)$
$=-1\cdot4$
$=-4$
$\text{#}Toru$
=57.(157-98-57):57 (bn đặt thừa số chung nhé)
=157-98-57=2 (sai thôi nhé mk ko bấm máy)
=\(=\frac{57\left(157-98-57\right)}{57}=2\)
A=[57(157-99-57)]:57+57= 57:57+57=58