Question

Tìm \(n\in N\)biết: \(x^3y^4+2x^3y^4+3x^3y^4+...+nx^3y^4=820x^3y^4\)

Answer 1

\(x^3y^4+2x^3y^4+3x^3y^4+....+nx^3y^4=820x^3y^4\)

\(\Leftrightarrow x^3y^4\left(1+2+3+....+n\right)=820x^3y^4\)

\(\Leftrightarrow1+2+3+....+n=820\)

\(\Leftrightarrow\frac{n\left(n+1\right)}{2}=820\)

\(\Leftrightarrow n\left(n+1\right)=1640=40.41\)

\(\Rightarrow n=40\)

Answer 2

\(x^3y^4+2x^3y^4+3x^3y^4+...+nx^3y^4=820x^3y\)

\(\Leftrightarrow x^3y^4\left(1+2+3+...+n\right)=820x^3y^4\)

\(\Leftrightarrow1+2+3+...+n=820\)

\(\Leftrightarrow\frac{n\left(n+1\right)}{2}=820\)

\(\Leftrightarrow n\left(n+1\right)=1640=40,61\)

\(n=40\)