a) (-49).99
b) (-52).(-101)
1.tính nhanh : cách giải nhé !
a) (-49).99
b)(-52) . (-101)
mình đang vội , nhanh nhé
a) (-49).(100-1)=(-49).100+49=-4900+49=-4851
b) (-52).(-101)= (-52).{(-100)-1}=(-52).(-100)-(-52)=5200+52=5252
A = 1 . 2 + 2 . 3 + 3 . 4 + ......... + 98 . 99 / 1 + ( 1 + 2 ) + ( 1 + 2 + 3 ) + ........... + ( 1 + 2 + 3 + ...... + 98 )
B = ( 1 / 51 . 52 ) + 1 / 52 . 53 + ...... + 1 / 100 . 101 ) : ( 1 / 1 . 2 + 1 / 2 . 3 + ........ + 1 / 99 . 100 + 1 / 100 . 101
3+5+7+9+…..+99+101 + 52 . 13
Xét tổng : `3+5+7+...+101`
Số số hạng dãy số trên :
`(101-3):2+1=50` (số hạng)
Tổng dãy trên có giá trị :
\(\left(101+3\right).50:2=52.50\)
Ta có : `3+5+7+9+...+99+101+52.13`
`=52.50+52.13`
`=52.(50+13)`
`=52.63`
`=3276
\(3+5+7+9+11+...+101+52\cdot13\)
\(=3+5+7+9+11+...+101+676\)
\(=(101+3)+(99+5)+(97+7)+...+676\)
\(=(101+3)*\dfrac{(101-3):2+1}{2}+676\)
\(=104*25+676=2600+676=3276\)
\(A=\frac{100^2+1^2}{100.1}+\frac{99^2+2^2}{99.2}+...+\frac{52^2+49^2}{52.49}+\frac{51^2+50^2}{51.50}\)
\(B=\frac{1}{100.1}+\frac{1}{99.2}+...+\frac{1}{51.50}\)
\(C=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}+\frac{1}{101}\)
a) Tính\(\frac{A}{C}\)
b)Tính C-101B
Tính B=1*3+5*7+9*11+...+97*101
C=1*3*5-3*5*7+5*7*9-....-97*99*101
D=1*99+3*97+5*95+...+49*51
E=1*3^3+3*5^3+5*7^3+...+49*51^3
F=1*99^2+2*98^2+3*97^2+...+49*51^2
cái này bạn mở sách bồi dưỡng toán ra trang gần cuối là thấy ngay ấy mà
cho E = \(\frac{100^2+1^2}{100.1}+\frac{99^2+2^2}{99.2}+\frac{98^2+3^2}{98.3}+...+\frac{52^2+49^2}{52.49}+\frac{50^2+49^2}{50.49}\)
F = \(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}+\frac{1}{101}\)
Hãy tính E/F
\(\frac{E}{F}=\frac{5}{2}\) Chỉ nhớ kết quả thôi Hoàng Minh Đ.... à !
Tính nhanh
a,A=3/1×3 +3/3×5 + ......+ 3/49×51
b,(1+1/1×3)×(1+1/2×4)×(1+1/3×5)×.......×(1+1/99×101)
\(\)\(A=\frac{3}{1\times3}+\frac{3}{3\times5}+...+\frac{3}{49\times51}\)
\(\Leftrightarrow A=\frac{3}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{51}\right)\)
\(\Leftrightarrow A=\frac{3}{2}.\left(1-\frac{1}{51}\right)\)
\(\Leftrightarrow A=\frac{3}{2}.\frac{50}{51}\)
\(\Leftrightarrow A=\frac{25}{17}\)
\(\)\(\)
\(\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)...\left(1+\frac{1}{99\cdot101}\right)\)
\(=\frac{4}{1\cdot3}\cdot\frac{9}{2\cdot4}\cdot\frac{16}{3\cdot5}\cdot...\cdot\frac{10000}{99\cdot101}\)
\(=\frac{\left(2\cdot2\right)\left(3\cdot3\right)\left(4\cdot4\right)\cdot...\cdot\left(100\cdot100\right)}{\left(1\cdot3\right)\left(2\cdot4\right)\left(3\cdot5\right)\cdot...\cdot\left(99\cdot101\right)}\)
\(=\frac{\left(2\cdot3\cdot4\cdot...\cdot100\right)\left(2\cdot3\cdot4\cdot...\cdot100\right)}{\left(1\cdot2\cdot3\cdot...\cdot99\right)\left(3\cdot4\cdot5\cdot...\cdot101\right)}\)
\(=\frac{100\cdot2}{1\cdot101}\)
\(=\frac{200}{101}\)
Tính: \(B=\frac{100^2+1^2}{100\cdot1}+\frac{99^2+2^2}{99\cdot2}+\frac{98^2+3^2}{98\cdot3}+...+\frac{52^2+49^2}{52\cdot49}+\frac{51^2+50^2}{51\cdot50}\)
1) Tính nhanh:
a, 125 x 3 + 125 x 125 x 6
b, ( 245 x 99 + 245 ) - ( 145 x 101 - 145 )
c, 154 x ( 28 + 52 ) - 45 x ( 26 + 54 )
a) 125.3+125.125.6
=125.3+125.750
=125.(3+750)
=125.753
=94125
b) (245.99+245)-(145.101-145)
=(245.(99+1))-(145.(101-1))
=245.100-145.100
=(245-145).100
=100.100
=10000
c) 154.(28+52)-45.(26+54)
=154.80-45.80
=(154-45).80
=109.80
=8720
a) 125x3+125+125x6
=125x(3+1+6)
=125x10
=1250
b) (245x99+245)-(145x101-145)
=(245x99+245)-(145x100)
=(245x100)-14500
=24500-14500
10000
c) 154x80-45x80
=80x(145-45)
=80x100
=8000
a, 125 x 3 + 125 x 125 x 6
=125 x 3 + 125 x 750
=125 x( 3+750)
=125 x753
=94125
b, ( 245 x 99 + 245 ) - ( 145 x 101 - 145 )
=[245 x ( 99+1 )] - [145 x ( 101-1 )]
=( 245 x 100 ) - ( 145 x 100 )
=24500 - 14500
=10 000
c, 154 x ( 28 + 52 ) - 45 x ( 26 + 54 )
=154 x 80 - 45 x 80
=(154-45)x80
=109 x80
=8720