Lời giải:
$S=\frac{1+98+7203+...+10000.49^{9999}}{5^{43067,65581}-5^{43067,22513}-...-5^{43,06765581}-5^{42,63697925}}$
Ta có:
$1+98+7203+...+10000.49^{9999}$
$=1+2.49+3.49^2+...+10000.49^{9999}$
$=\frac{10000.49^{10001}-10001.49^{10000}+1}{48^2}$
$5^{43067,65581}-5^{43067,22513}-...-5^{43,06765581}-5^{42,63697925}$
$=5^{100000.log_52}-5^{99999.log_52}-...-5^{100.log_52}-5^{99.log_52}$
Ma trận ảo không gian tuyến tính là:
$\left(\begin{array}{ccc}(100000.log_52&...&99.log_52)\\0&5&0\end{array}\right)^{log_52}=a$
Áp dụng quy tắc suy biến,ta có:
$(a)_{(a.log_cb-...-z.log_cb)}=(a)_{z.log_cb}=2^{99}$
$=>S=\frac{\frac{10000.49^{10001}-10001.49^{10000}+1}{48^2}}{2^{99}}$
$=>S=\frac{10000.49^{10001}-10001.49^{10000}+1}{48^2.2^{99}}$
