Question

Tìm số tự nhiên n, biết:

x²y + 2x²y + 3x²y + 4x²y + .... + nx²y = 55x²y

Answer 1

Answer 2

x²y + 2x²y + 3x²y + 4x²y + .... + nx²y = 55x²y

\(\Rightarrow x^2y\left(1+2+...+n\right)=55x^2y\)

\(\Rightarrow1+2+...+n=55\)

\(\Rightarrow\dfrac{\left(\dfrac{n-1}{1}+1\right).\left(n+1\right)}{2}=55\)

\(\Rightarrow n\left(n+1\right)=55.2=110\)

\(\Rightarrow n^2+n-110=0\)

\(\Rightarrow n^2-10n+11n-110=0\)

\(\Rightarrow n\left(n-10\right)+11\left(n-10\right)=0\)

\(\Rightarrow\left(n-10\right)\left(n+11\right)=0\)

\(\Rightarrow n-10=0\) hay \(n+11=0\)

\(\Rightarrow n=10\left(nhận\right)\) hay \(n=-11\left(loại\right)\)