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解答 - 几何数列

公比是：

r = 0.0010834236186348862

r=0.0010834236186348862

该系列的和是：

s = 924

s=924

此系列的通用形式是：

a_{n} = 923 \cdot {0.0010834236186348862}^{n - 1}

a_n=923*0.0010834236186348862^(n-1)

这个序列的第n项是：

923, 1, 0.0010834236186348862, 1.1738067374159113 E - 06, 1.2717299430291561 E - 09, 1.3778222568029862 E - 12, 1.4927651753011765 E - 15, 1.617297047996941 E - 18, 1.752217820148365 E - 21, 1.898394171341674 E - 24

923,1,0.0010834236186348862,1.1738067374159113E-06,1.2717299430291561E-09,1.3778222568029862E-12,1.4927651753011765E-15,1.617297047996941E-18,1.752217820148365E-21,1.898394171341674E-24

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：

$a_{2} a_{1} = \frac{1}{923} = 0.0010834236186348862$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.0010834236186348862$

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： $a = 923$ 、公比： $r = 0.0010834236186348862$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 923 * ((1 - {0.0010834236186348862}^{2}) / (1 - 0.0010834236186348862))$

$s_{2} = 923 * ((1 - 1.1738067374159113 E - 06) / (1 - 0.0010834236186348862))$

$s_{2} = 923 * (0.9999988261932626 / (1 - 0.0010834236186348862))$

$s_{2} = 923 * (0.9999988261932626 / 0.9989165763813651)$

$s_{2} = 923 \cdot 1.001083423618635$

$s_{2} = 924.0000000000001$

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： $a = 923$ 和公比： $r = 0.0010834236186348862$ 插入几何级数的公式：

$a_{n} = 923 \cdot {0.0010834236186348862}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 923$

$a_{2} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{2 - 1} = 923 \cdot {0.0010834236186348862}^{1} = 923 \cdot 0.0010834236186348862 = 1$

$a_{3} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{3 - 1} = 923 \cdot {0.0010834236186348862}^{2} = 923 \cdot 1.1738067374159113 E - 06 = 0.0010834236186348862$

$a_{4} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{4 - 1} = 923 \cdot {0.0010834236186348862}^{3} = 923 \cdot 1.2717299430291563 E - 09 = 1.1738067374159113 E - 06$

$a_{5} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{5 - 1} = 923 \cdot {0.0010834236186348862}^{4} = 923 \cdot 1.3778222568029862 E - 12 = 1.2717299430291561 E - 09$

$a_{6} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{6 - 1} = 923 \cdot {0.0010834236186348862}^{5} = 923 \cdot 1.4927651753011767 E - 15 = 1.3778222568029862 E - 12$

$a_{7} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{7 - 1} = 923 \cdot {0.0010834236186348862}^{6} = 923 \cdot 1.617297047996941 E - 18 = 1.4927651753011765 E - 15$

$a_{8} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{8 - 1} = 923 \cdot {0.0010834236186348862}^{7} = 923 \cdot 1.752217820148365 E - 21 = 1.617297047996941 E - 18$

$a_{9} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{9 - 1} = 923 \cdot {0.0010834236186348862}^{8} = 923 \cdot 1.898394171341674 E - 24 = 1.752217820148365 E - 21$

$a_{10} = a_{1} \cdot r^{n - 1} = 923 \cdot {0.0010834236186348862}^{10 - 1} = 923 \cdot {0.0010834236186348862}^{9} = 923 \cdot 2.0567650827103723 E - 27 = 1.898394171341674 E - 24$

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几何数列