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解答 - 几何数列

公比是：

r = 0.030303030303030304

r=0.030303030303030304

该系列的和是：

s = 34

s=34

此系列的通用形式是：

a_{n} = 33 \cdot {0.030303030303030304}^{n - 1}

a_n=33*0.030303030303030304^(n-1)

这个序列的第n项是：

33, 1, 0.030303030303030307, 0.0009182736455463729, 2.7826474107465846 E - 05, 8.432264881050256 E - 07, 2.5552317821364416 E - 08, 7.743126612534672 E - 10, 2.3464020037983852 E - 11, 7.110309102419349 E - 13

33,1,0.030303030303030307,0.0009182736455463729,2.7826474107465846E-05,8.432264881050256E-07,2.5552317821364416E-08,7.743126612534672E-10,2.3464020037983852E-11,7.110309102419349E-13

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：

$a_{2} a_{1} = \frac{1}{33} = 0.030303030303030304$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.030303030303030304$

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： $a = 33$ 、公比： $r = 0.030303030303030304$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 33 * ((1 - {0.030303030303030304}^{2}) / (1 - 0.030303030303030304))$

$s_{2} = 33 * ((1 - 0.0009182736455463729) / (1 - 0.030303030303030304))$

$s_{2} = 33 * (0.9990817263544536 / (1 - 0.030303030303030304))$

$s_{2} = 33 * (0.9990817263544536 / 0.9696969696969697)$

$s_{2} = 33 \cdot 1.0303030303030303$

$s_{2} = 34$

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： $a = 33$ 和公比： $r = 0.030303030303030304$ 插入几何级数的公式：

$a_{n} = 33 \cdot {0.030303030303030304}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 33$

$a_{2} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{2 - 1} = 33 \cdot {0.030303030303030304}^{1} = 33 \cdot 0.030303030303030304 = 1$

$a_{3} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{3 - 1} = 33 \cdot {0.030303030303030304}^{2} = 33 \cdot 0.0009182736455463729 = 0.030303030303030307$

$a_{4} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{4 - 1} = 33 \cdot {0.030303030303030304}^{3} = 33 \cdot 2.7826474107465846 E - 05 = 0.0009182736455463729$

$a_{5} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{5 - 1} = 33 \cdot {0.030303030303030304}^{4} = 33 \cdot 8.432264881050256 E - 07 = 2.7826474107465846 E - 05$

$a_{6} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{6 - 1} = 33 \cdot {0.030303030303030304}^{5} = 33 \cdot 2.5552317821364412 E - 08 = 8.432264881050256 E - 07$

$a_{7} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{7 - 1} = 33 \cdot {0.030303030303030304}^{6} = 33 \cdot 7.743126612534672 E - 10 = 2.5552317821364416 E - 08$

$a_{8} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{8 - 1} = 33 \cdot {0.030303030303030304}^{7} = 33 \cdot 2.3464020037983852 E - 11 = 7.743126612534672 E - 10$

$a_{9} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{9 - 1} = 33 \cdot {0.030303030303030304}^{8} = 33 \cdot 7.110309102419349 E - 13 = 2.3464020037983852 E - 11$

$a_{10} = a_{1} \cdot r^{n - 1} = 33 \cdot {0.030303030303030304}^{10 - 1} = 33 \cdot {0.030303030303030304}^{9} = 33 \cdot 2.1546391219452575 E - 14 = 7.110309102419349 E - 13$

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几何数列