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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]
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 
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 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.txt · Last modified: 2014/10/17 10:23 by gibson