Question

( x + 1 ) + ( x + 2 ) + ( x + 3 ) + .... + ( x + 100) = 5550

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Answer 1

(x+1)+(x+2)+(x+3)+...+(x+100)=5550
=> 100x + (1+2+...+100) = 5550
=> x = [ 5550 - (1+2+...+100) ]/100
=> x = (5550 - 5050) / 100
=> x = 5

Answer 2

\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5550\Leftrightarrow100x+1+2+...+100=5550\)5550 (1)

\(1+2+3+...+100=\frac{100.\left(100+1\right)}{2}=5050\)(2)

Từ 1 và 2 suy ra: 100x=5550-5050=500 => x=5

Answer 3

\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5550.\)

\(\Leftrightarrow\frac{\left[\left(x+1\right)+\left(x+100\right)\right].\left\{\left[\left(x+100\right)-\left(x+1\right)\right]+1\right\}}{2}=5550\)

\(\Leftrightarrow\frac{2x+101.100}{2}=5550\)

\(\Leftrightarrow2x+101.100=11100\)

\(\Leftrightarrow2x+101=111\)

\(\Leftrightarrow2x=10\)

\(\Leftrightarrow x=5\)