Question

\(x^2y+2x^2y+3x^2y+...+nx^2y=210x^2y\)

Answer 1

\(x^2y+2x^2y+3x^2y+....+nx^2y=210x^2y\)

\(x^2y\left(1+2+3+...+n\right)=210x^2y\)

\(1+2+3+...+n=210\)

\(\frac{n\left(n+1\right)}{2}=210\)

\(n\left(n+1\right)=420\)

\(n\left(n+1\right)=20.21\)

\(\Rightarrow n=20\)

Answer 2

x^2.y+2x^2.y+3x^2.y+...+n.x^2y=210x^2.y

x^2.y(1+2+3+..+n)=210x^2.y

1+2+3+..+n=210

=>(n+1)(n-1+1)/2=210

(n+1)n/2=210

(n+1)n=420=21.20

=>n+1=21

n=20