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解答 - 几何数列

公比是：

r = 0.010582010582010581

r=0.010582010582010581

该系列的和是：

s = 2865

s=2865

此系列的通用形式是：

a_{n} = 2835 \cdot {0.010582010582010581}^{n - 1}

a_n=2835*0.010582010582010581^(n-1)

这个序列的第n项是：

2835, 30, 0.31746031746031744, 0.003359368438733518, 3.554887236755045 E - 05, 3.761785435719624 E - 07, 3.980725328803835 E - 09, 4.212407755347973 E - 11, 4.457574344283569 E - 13, 4.717009888130761 E - 15

2835,30,0.31746031746031744,0.003359368438733518,3.554887236755045E-05,3.761785435719624E-07,3.980725328803835E-09,4.212407755347973E-11,4.457574344283569E-13,4.717009888130761E-15

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：

$a_{2} a_{1} = \frac{30}{2835} = 0.010582010582010581$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.010582010582010581$

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： $a = 2, 835$ 、公比： $r = 0.010582010582010581$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 2835 * ((1 - {0.010582010582010581}^{2}) / (1 - 0.010582010582010581))$

$s_{2} = 2835 * ((1 - 0.00011197894795778393) / (1 - 0.010582010582010581))$

$s_{2} = 2835 * (0.9998880210520422 / (1 - 0.010582010582010581))$

$s_{2} = 2835 * (0.9998880210520422 / 0.9894179894179894)$

$s_{2} = 2835 \cdot 1.0105820105820107$

$s_{2} = 2865.0000000000005$

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： $a = 2, 835$ 和公比： $r = 0.010582010582010581$ 插入几何级数的公式：

$a_{n} = 2835 \cdot {0.010582010582010581}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 2835$

$a_{2} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{2 - 1} = 2835 \cdot {0.010582010582010581}^{1} = 2835 \cdot 0.010582010582010581 = 30$

$a_{3} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{3 - 1} = 2835 \cdot {0.010582010582010581}^{2} = 2835 \cdot 0.00011197894795778393 = 0.31746031746031744$

$a_{4} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{4 - 1} = 2835 \cdot {0.010582010582010581}^{3} = 2835 \cdot 1.1849624122516818 E - 06 = 0.003359368438733518$

$a_{5} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{5 - 1} = 2835 \cdot {0.010582010582010581}^{4} = 2835 \cdot 1.2539284785732081 E - 08 = 3.554887236755045 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{6 - 1} = 2835 \cdot {0.010582010582010581}^{5} = 2835 \cdot 1.3269084429346117 E - 10 = 3.761785435719624 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{7 - 1} = 2835 \cdot {0.010582010582010581}^{6} = 2835 \cdot 1.4041359184493245 E - 12 = 3.980725328803835 E - 09$

$a_{8} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{8 - 1} = 2835 \cdot {0.010582010582010581}^{7} = 2835 \cdot 1.4858581147611898 E - 14 = 4.212407755347973 E - 11$

$a_{9} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{9 - 1} = 2835 \cdot {0.010582010582010581}^{8} = 2835 \cdot 1.5723366293769203 E - 16 = 4.457574344283569 E - 13$

$a_{10} = a_{1} \cdot r^{n - 1} = 2835 \cdot {0.010582010582010581}^{10 - 1} = 2835 \cdot {0.010582010582010581}^{9} = 2835 \cdot 1.663848285054942 E - 18 = 4.717009888130761 E - 15$

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几何数列