gibson:teaching:fall-2014:math445:lecture10-diary
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gibson:teaching:fall-2014:math445:lecture10-diary [2014/10/17 10:22] gibson |
gibson:teaching:fall-2014:math445:lecture10-diary [2014/10/17 10:23] (current) gibson |
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| We can also do the sum with a ''for'' loop. To see how to build the ''for'' loop, it's helpful to think of the series as a sequence of //partial sums// | We can also do the sum with a ''for'' loop. To see how to build the ''for'' loop, it's helpful to think of the series as a sequence of //partial sums// | ||
| - | \begin{eqnarray*} | ||
| - | P_N = \sum_{n=1}^{N} \frac{1}{n^2} | ||
| - | \end{eqnarray*} | ||
| \begin{eqnarray*} | \begin{eqnarray*} | ||
| P_1 = 1 | P_1 = 1 | ||
| Line 26: | Line 23: | ||
| P_3 = 1 + \frac{1}{2^2} + \frac{1}{3^2} | P_3 = 1 + \frac{1}{2^2} + \frac{1}{3^2} | ||
| \end{eqnarray*} | \end{eqnarray*} | ||
| - | The Nth partial sum $P_N$ is | + | etc. Note that the difference between successive partial sums is a single term. |
| - | \begin{eqnarray*} | + | |
| - | P_N = \sum_{n=1}^{N} \frac{1}{n^2} | + | |
| - | \end{eqnarray*} | + | |
| - | Note that the difference between successive partial sums is a single term. | + | |
| \begin{eqnarray*} | \begin{eqnarray*} | ||
| P_n = P_{n-1} + \frac{1}{n^2} | P_n = P_{n-1} + \frac{1}{n^2} | ||
gibson/teaching/fall-2014/math445/lecture10-diary.1413566534.txt.gz · Last modified: 2014/10/17 10:22 by gibson
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