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Tìm x, biết:
a) (x + 1) + (x + 2) + (x + 3) + ... + (x + 100) = 205550
b) 3x + 3x + 1 + 3x + 2 = 351
a)(x+x+x+...+x)+(1+2+3+...+100)=205550
100x + 5050 =205550
100x =205550 - 5050
100x =200500
x =200500 : 100
x =2005
a, => 3x-17 = 0 hoặc 3x-17 = 1
=> x=17/3 hoặc x=6
b, => x+1+x+2+....+x+100=205550
=>100x + (1+2+...+100)=205550
=> 100x + 5050 = 205550
=> 100x = 205550 - 5050 = 200500
=>x= 2005
c,=>x+x+1+....+x+2010=2029099
=>2011x+(1+2+....+2010)=2029099
=>2011x+2021055=2029099
=>2011x = 2029099-2021055 = 8044
=>x=4
Có : 3Q = 3+3^2+....+3^101
2Q=3Q-Q= (3+3^2+....+3^101)-(1+3+3^2+...+3^100) = 3^101-1
=>Q = (3^101-1)/2
1a)1+2+3+...+x=0
\(\frac{x.\left(x+1\right)}{2}\)=0
x.(x+1) =0:2
x.(x+1) =0
x.(x+1) =0.1
vây x=0
tich dung cho minh nha
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
mình đg cần gấp á
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: \(x=40\)
c) \(3^{x+1}=9\cdot27\)
\(\Rightarrow3^{x+1}=3^2\cdot3^3\)
\(\Rightarrow3^{x+1}=3^5\)
\(\Rightarrow x+1=5\)
\(\Rightarrow x=4\)
d) \(x+2x+3x+...+100x=15150\)
\(\Rightarrow x\cdot\left(1+2+3+4+...+100\right)=15150\)
\(\Rightarrow x\cdot5050=15150\)
\(\Rightarrow x=15150:505\)
\(\Rightarrow x=3\)
e) \(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=205550\)
\(\Rightarrow x+1+x+2+...+x+100-205550\)
\(\Rightarrow x\cdot100+5050=205550\)
\(\Rightarrow x\cdot100=205550-505\)
\(\Rightarrow x\cdot100=200500\)
\(\Rightarrow x=200500:100\)
\(\Rightarrow x=2005\)
f) \(3^x+3^{x+1}+3^{x+2}=351\)
\(\Rightarrow3^x\cdot\left(1+3^1+3^2\right)=3501\)
\(\Rightarrow3^x\cdot13=351\)
\(\Rightarrow3^x=351:13\)
\(\Rightarrow3^x=27\)
\(\Rightarrow3^x=3^3\)
\(\Rightarrow x=3\)