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Đề sai rồi! Đề đúng là : (x+1)+(x+2)+......+(x+100)=5750
=> (x+x+x+.....+x) + (1+2+3+......+100) = 5750
=> 100x + 5050 = 5750
=> 100x = 700
=> x = 7 (tm)
Vậy...................
\(c,\)\(\left(x-1\right)+\left(x-2\right)+....+\left(x-100\right)=50\)
\(\left(x+x+...+x\right)-\left(1+2+...+100\right)=50\)
\(100x-5050=50\)
\(100x=50+5050\)
\(100x=5100\)
\(\Rightarrow x=\frac{5100}{100}=51\)
\(a,\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+100\right)=5750\)
\(\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
\(100x+5050=5750\)
\(100x=5750-5050\)
\(100x=700\)
\(\Rightarrow x=7\)
\(b,x+\left(1+2+3+...+50\right)=2000\)
\(x+\frac{\left[1+50\right]\cdot\left[\left(50-1\right)\div1+1\right]}{2}=2000\)
\(x+1275=2000\)
\(\Rightarrow x=2000-1275=725\)
Ta có: \(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
\(\Leftrightarrow100x+5050=5750\)
\(\Leftrightarrow100x=700\)
hay x=7
(x+1) + (x+2) + (x+3) +....+ (x+100) = 5750
x + 1 + x + 2 + x + 3 +...+ x + 100 = 5750
(x + x + x +...+ x) + (1 + 2 + 3 +...+ 100) = 5750
100x + 5050 = 5750
100x = 5750 - 5050
100x = 700
x = 700 : 100
x = 7
x(x+1)+(x+2)+(x+3)+...+(x+100)=5750
=> (x+x+x+x+...+x)+(1+2+3+...+100)=5750
=> 101x+5050=5750
101x = 5750-5050
101x = 700
x = 700 : 101
x = 700/101
x+x+x+...x+ 1+2+3+...100 = 5750
100.x + 101.50 = 5750
100.x = 5757-5050
100.x = 700
x = 700: 100
x = 7
a) Dãy trên có số số hạng là :
( x - 1 ) : 1 + 1 = ( x - 1 ) + 1 = x
=> 1 + 2 + 3 + 4 + ... + x = 45
=> ( x + 1 ) . x : 2 = 45
=> ( x + 1 ) . x = 90
=> ( x + 1 ) . x = 10 . 9
=> x = 9
Vậy x = 9
a) Dãy trên có số số hạng là :
( x - 1 ) : 1 + 1 = ( x - 1 ) + 1 = x
=> 1 + 2 + 3 + 4 + ... + x = 45
=> ( x + 1 ) . x : 2 = 45
=> ( x + 1 ) . x = 90
=> ( x + 1 ) . x = 10 . 9
=> x = 9
Vậy x = 9
(x + 1) + (x + 2) + (x + 3) + ... + (x + 100) = 5750
=> x + 1 + x + 2 + x + 3 + ... + x + 100 = 5750
=> (x + x + x + .... + x) + (1 + 2 + 3 + 4 + ... + 100) = 5750 (100 số hạng x)
=> 100x + \(\left[\left(100-1\right):1+1\right].\left(\frac{100+1}{2}\right)\) = 5750
=> 100x + \(100.\frac{101}{2}\)= 5750
=> 100x + 5050 = 5750
=> 100x = 5750 - 5050
=> 100x = 700
=> x = 700 : 100
=> x = 7
\(a.x\left(x+3\right)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\x+3=0\Leftrightarrow x=-3\end{cases}}\)
\(b,\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
\(100x+\left(1+2+...+100\right)=5750\)
\(100x+\frac{100.101}{2}=5750\)
\(100x+5050=5750\)
\(100x=200\Leftrightarrow x=2\)
a) \(x.\left(x+3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x+3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=-3\end{cases}}\)
b) (x + 1) + (x + 2) + ... + (x + 100) = 5750
(x + x + .... + x) + (1 + 2 + .. + 100) = 5750
100x + 5050 = 5750
100x = 5750 - 5050
100x = 700
x = 700 : 100 = 7