Question

Tìm x, biết:
x + 2x + 3x + ... + 1000x = 5005 . 10⁴

Answer 1

x+2x+3x+...+1000x=5005x\(10^4\)

ta có:x+2x+3x+...+1000x=x(1+2+3+...+1000)

                                     =x((1000+1):2x1000)

                                     =x500500

\(\Rightarrow\) x500500=5005x\(10^4\) 

x5005.\(100\)=5005x\(10^4\) 

x5005.\(10^2\)=5005x\(10^4\) 

\(\Rightarrow x.10^2=10^4\)

x=\(10^4:10^2\)

x=\(10^2\) 

x=100