อ้างอิง:
ข้อความเดิมเขียนโดยคุณ Amankris
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4). Simplify $\dfrac{3^3}{2}-\dfrac{5^3}{6}+\dfrac{7^3}{12}-\dfrac{9^3}{20}+\dfrac{11^3}{30}-\dfrac{13^3}{42}+\dfrac{15^3}{56}-\dfrac{17^3}{72}+\ldots+\dfrac{199^3}{9900}$
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$=3^2(1+\frac{1}{2} )-5^2(\frac{1}{2}+ \frac{1}{3} )+7^2(\frac{1}{3} +\frac{1}{4})-9^2(\frac{1}{4}+\frac{1}{5})+...-193^2(\frac{1}{96}+\frac{1}{97})+195^2(\frac{1}{97}+\frac{1}{98})-197^2(\frac{1}{98}+\frac{1}{99})+199^2(\frac{1}{99}+\frac{1}{100})$
$=3^2+\frac{3^2}{2} -\frac{5^2}{2} -\frac{5^2}{3}+\frac{7^2}{3}+\frac{7^2}{4}-\frac{9^2}{4}-\frac{9^2}{5}+...-\frac{193^2}{96}-\frac{193^2}{97}+\frac{195^2}{97}+\frac{195^2}{98}-\frac{197^2}{98}-\frac{197^2}{99}+\frac{199^2}{99}+\frac{199^2}{100}$
$=3^2-8+8-8+8-8+...+8-8+8-8+8+\frac{199^2}{100}$
$=3^2+\frac{199^2}{100}$
$=\frac{40501}{100} =405.01$ครับ