ตอนที่2 อัตนับเติมคำตอบ ข้อ 11
$a = \frac{1}{4 \cdot 7} + \frac{1}{7 \cdot 10} + \frac{1}{10 \cdot 13} + ... + \frac{1}{76 \cdot 79}$
$ = \frac{1}{3}[(\frac{1}{4} - \frac{1}{7})+(\frac{1}{7} - \frac{1}{10})+(\frac{1}{10} - \frac{1}{13}) + ... +(\frac{1}{76} - \frac{1}{79})]$
$ = \frac{1}{3}(\frac{1}{4} - \frac{1}{79}) = \frac{25}{316} \approx 0. 079$
$b = \frac{999999}{\sqrt{1002001} } = \frac{999999}{1001} = 999$
$c = \sqrt{12760^2 -10208^2 -76565^2} = \sqrt{(22968 \times 2552) - 7656^2} = \sqrt{3^2 \times 2552^2 - 3^2 \times 2552^2} = 0 $
$d = (1+5+9+13+...397+)+(2+6+10+14+...+398)+(3+7+11+15+...+399)-(2+8+12+16+...+400)$
$ = (1+2+3+...+400)-(4+8+12+16+...+400)-(2+8+12+16+...+400)$
$ = 80200 - 20200 - 20200+2 =39802$
$e = \frac{1}{\sqrt{2} +\sqrt{5} } + \frac{1}{\sqrt{5} +\sqrt{8} } + \frac{1}{\sqrt{8} +\sqrt{11} } + ... + \frac{1}{\sqrt{29} +\sqrt{32} }$
$ = - \frac{1}{3}[ (\sqrt{2} -\sqrt{5} ) + (\sqrt{5} -\sqrt{8} ) +(\sqrt{8} -\sqrt{11} ) + ...+ (\sqrt{29} -\sqrt{32} ) ]$
$ = -\frac{1}{3}(\sqrt{2} -\sqrt{32} ) = \sqrt{2} \approx 1.414 $
$a+b+c+d+e = 0. 079 + 999+0+ 39802 + 1.414 = 40802.493$
ตอบ 40802