Cho (1+x) + (2+x) + (3+x) + ... + (100+x) = 5060
Tìm x ?
Cho A = 1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 + ... + 100 x 101
và B = 1 x 3 + 2 x 4 + 3 x 5 + 4 x 6 + ... + 100 x 102
Vậy B - A = ?
Ta có : A = 1.2 + 2.3 + 3.4 + ...... + 100.101
=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 100.101.102
=> 3A = 100.101.102
=> A = 100.101.102/3
=> A = 343400
Cho x1+x2+x3+...+x100+x101=0. Biết x1+x2=x3+x4=...=x99+x100=x100+x101=1. Tính x100
Tính x1 + x2 +...+ x99 + x100 + x101 = 0
(x1 + x2)+ ...+ ( x99 + x100)+ x101 = 0
1 + ... + 1 + x101 = 0
1 x 50 + x101 = 0
50 + x101 = 0
x101 = 0 - 50
x101 = -50
Ta có: x100 + x101 = 1
x100 + (-50) = 1
x100 = 1-(-50)
x100 =51
Vậy x101 = 51
Cho f(x) = (x+3)(x+5)(x+7)(x+9)+2018 tìm dư trong phép chia f(x) cho x2+12x+32
CMR: 13+23+33+......+1003 chia hết cho B= 1+2+3+.......+100
Cho
x1+x2+x3+....+x100+x101=0
biết rằng x1+x2=x3+x4=....x100+x101=1
Tính x100
1 x 2 + 2 x 3 + 3 x 4 + ... + 100 x 101 =
1 x 2 x 3 + 2 x 3 x 4 + ... + 100 x 101 x 102
Có cả lời giải nhé
a: S=1(1+1)+2(1+2)+...+100(1+100)
=1+2+...+100+1^2+2^2+...+100^2
\(=\dfrac{100\cdot102}{2}+\dfrac{100\cdot\left(100+1\right)\cdot\left(2\cdot100+1\right)}{6}\)
\(=100\cdot51+\dfrac{100\cdot101\cdot201}{6}\)
=343450
b: \(A=1\cdot2\cdot3+2\cdot3\cdot4+...+100\cdot101\cdot102\)
=>\(4\cdot A=1\cdot2\cdot3\cdot\left(4-0\right)+2\cdot3\cdot4\left(5-1\right)+...+100\cdot101\cdot102\left(103-99\right)\)
=>4*A=100*101*102*103
=>A=25*101*102*103
4 x 2 : 2 x 3 : 3 x 4 : 4 x........x 100 : 100 + 6 x 1 : 1 x 2 : 2 x 3 : 3 x 4 : 4 x........x 1000 : 1000 x4
giúp nhanh
Tính
a) (x-1/2)+(x-1/4)+(x-1/8)+...+(x-1/512)
Tìm x
a) (x-1/1×2)+(x-1/2×3)+...+(x-1/100×101)
b) (x-1)+(x-2)+(x-3)+...+(x-101)=5050
c) x+1/2+1/3+1/4+...+1/100=3/2+4/3+5/4++...+101/100
1/Tìm x,biết:
a)x+(x+1)+(x+2)+(x+3)+...+(x+99)+(x+100)=5555
b)1+2+3+4+...+x=820
c)3(x+1)=9.27
d)x+2x+3x+...+99x+100x=15150
e)(x+1)+(x+2)+(x+3)+...+(x+100)=205550
f)3x+3x+1+3x+2=351
a)x+(x+1)+(x+2)+(x+3)+...+(x+99)+(x+100)=5555
=> 101x +5050 = 5555
=> 101x = 505
=> x = 505 : 101 = 5
Vậy, x = 5
b)1+2+3+4+...+x=820
=> ( x+1) x :2 = 820
=> (x+1)x = 1640
Mà 1640 = 40 . 41
=> x = 40 ( vì {x+1} - x = 1)
Vậy, x = 40
c) 3x+1 = 9.27=243
=> 3x+1 = 35
=>x + 1 = 5
=> x = 4
Vậy, x=4
d) x+2x+3x+...+99x+100x=15150
=> [( 100 + 1) x 100 :2 ] x = 15150
=> 5050x = 15150
=> x = 15150:5050 = 3
Vậy, x =3
e)(x+1)+(x+2)+(x+3)+...+(x+100)=205550
=> 100x + 5050 = 205550
=> 100x = 205550 - 5050= 200500
=> x = 200500 : 100 = 2005
Vậy, x = 2005
f)3x+3x+1+3x+2=351
=> 3x + 3x . 3 + 3x x 9 = 351
=> 3x ( 1+3+9) = 351
=> 3x . 13 = 351
=> 3x = 351 :13=27 mà 27 = 33
=> x=3
Vậy, x=3
a) \(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5555\)
\(\Rightarrow x+x+1+x+2+x+3+...+x+100=5555\)
\(\Rightarrow101\cdot x+5050=5555\)
\(\Rightarrow101\cdot x=5555-5050\)
\(\Rightarrow101\cdot x=505\)
\(\Rightarrow x=505:101\)
\(\Rightarrow x=5\)
b) \(1+2+3+4+...+x=820\)
\(\Rightarrow\left(x+1\right)\cdot\left[\left(x-1\right):1+1\right]:2=820\)
\(\Rightarrow\left(x+1\right)\cdot\left(x+1-1\right):2=820\)
\(\Rightarrow\left(x+1\right)\cdot x:2=820\)
\(\Rightarrow x\cdot\left(x+1\right)=820\cdot2\)
\(\Rightarrow x\cdot\left(x+1\right)=1640\)
Ta thấy: \(40\cdot41=1640\)
Vậy: \(x=40\)
Bài 6 Tìm x
1) ( x+1 ) + ( x+2 ) + ( x+3 ) + ... + ( x+100 ) = 5750
2) ( 2x-1 ) + ( 4x-2 ) + ... + ( 200x - 100 ) = 5050
3) ( x+2 ) + ( x+4 ) + ( x+6 ) + ... + ( x + 100) = 2650
1) tìm x thuộc q biết :
a) 2^x + 2^x+1 + 2^x+2 = 448
b) 3^x+2 - 3^x+1 + 3^x = 18^9
2) Chứng tỏ rằng :
a) 5^14 + 5^15 + 6^16 chia hết cho 3
b) 3^1 + 3^2 + 3^3 +...+ 3^100 chia hết cho 100
Giúp mình làm với nha :)))
ukm
it 's very hard
l can do it
sorry!