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解答 - 几何数列

公比是：

r = - 9.990000099900002 E - 06

r=-9.990000099900002E-06

该系列的和是：

s = - 99999000

s=-99999000

此系列的通用形式是：

a_{n} = - 99999999 \cdot - 9.990000099900002 E - 06^{n - 1}

a_n=-99999999*-9.990000099900002E-06^(n-1)

这个序列的第n项是：

- 99999999, 999.0000000000001, - 0.009980010099800103, 9.970030189400607 E - 08, - 9.960060258811808 E - 13, 9.950100298053999 E - 18, - 9.940150297157451 E - 23, 9.930210246162396 E - 28, - 9.920280135119035 E - 33, 9.910359954087517 E - 38

-99999999,999.0000000000001,-0.009980010099800103,9.970030189400607E-08,-9.960060258811808E-13,9.950100298053999E-18,-9.940150297157451E-23,9.930210246162396E-28,-9.920280135119035E-33,9.910359954087517E-38

查看步骤

逐步解答

1. 找到公比

通过将序列中的任何项除以前一项来找到公比：

$a_{2} a_{1} = \frac{999}{-} 99999999 = - 9.990000099900002 E - 06$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = - 9.990000099900002 E - 06$

2. 求和

5 个额外步骤

$s_{n} = a * ((1 - r^{n}) / (1 - r))$

要找到系列的和，将第一项： $a = - 99999999$ 、公比： $r = - 9.990000099900002 E - 06$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = - 99999999 * ((1 - - 9.990000099900002 E - 06^{2}) / (1 - - 9.990000099900002 E - 06))$

$s_{2} = - 99999999 * ((1 - 9.980010199600204 E - 11) / (1 - - 9.990000099900002 E - 06))$

$s_{2} = - 99999999 * (0.9999999999001999 / (1 - - 9.990000099900002 E - 06))$

$s_{2} = - 99999999 * (0.9999999999001999 / 1.0000099900000998)$

$s_{2} = - 99999999 \cdot 0.9999900099999002$

$s_{2} = - 99999000.00000001$

3. 找到通用形式

$a_{n} = a \cdot r^{n - 1}$

要找到系列的通用形式，将第一项： $a = - 99999999$ 和公比： $r = - 9.990000099900002 E - 06$ 插入几何级数的公式：

$a_{n} = - 99999999 \cdot - 9.990000099900002 E - 06^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = - 99999999$

$a_{2} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{2 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{1} = - 99999999 \cdot - 9.990000099900002 E - 06 = 999.0000000000001$

$a_{3} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{3 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{2} = - 99999999 \cdot 9.980010199600204 E - 11 = - 0.009980010099800103$

$a_{4} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{4 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{3} = - 99999999 \cdot - 9.97003028910091 E - 16 = 9.970030189400607 E - 08$

$a_{5} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{5 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{4} = - 99999999 \cdot 9.960060358412411 E - 21 = - 9.960060258811808 E - 13$

$a_{6} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{6 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{5} = - 99999999 \cdot - 9.950100397555004 E - 26 = 9.950100298053999 E - 18$

$a_{7} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{7 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{6} = - 99999999 \cdot 9.940150396558955 E - 31 = - 9.940150297157451 E - 23$

$a_{8} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{8 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{7} = - 99999999 \cdot - 9.930210345464499 E - 36 = 9.930210246162396 E - 28$

$a_{9} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{9 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{8} = - 99999999 \cdot 9.920280234321838 E - 41 = - 9.920280135119035 E - 33$

$a_{10} = a_{1} \cdot r^{n - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{10 - 1} = - 99999999 \cdot - 9.990000099900002 E - 06^{9} = - 99999999 \cdot - 9.910360053191118 E - 46 = 9.910359954087517 E - 38$

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几何数列