[lnพwsะบุ๑sสุ๑xล่o]

$a_1+a_2+a_3+...+a_n=n^2a_n$

$n=1,2,3,....$

$a_1=100$ แล้ว $\lim_{x \to \infty} n^2a_n=?$

$Sol^n$

$a_1=100$

$a_2=\frac{100}{3} =\frac{100}{1+2} $

$a_3=\frac{100}{6} =\frac{100}{1+2+3} $

...

$a_n=\frac{100}{1+2+3+...+n} =\frac{200}{n(n+1)} $

$\lim_{x \to \infty} n^2a_n=\lim_{x \to \infty} \frac{200n}{n+1} =200$