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 gibson:teaching:fall-2014:math445:lecture10-diary [2014/10/17 10:23]gibson gibson:teaching:fall-2014:math445:lecture10-diary [2014/10/17 10:23] (current)gibson Both sides previous revision Previous revision 2014/10/17 10:23 gibson 2014/10/17 10:23 gibson 2014/10/17 10:22 gibson 2014/10/17 10:14 gibson 2014/10/17 09:44 gibson 2014/10/15 13:12 gibson 2014/10/15 13:04 gibson 2014/10/15 13:01 gibson 2014/10/15 12:55 gibson 2014/10/15 12:53 gibson 2014/10/15 12:53 gibson 2014/10/15 12:52 gibson 2014/10/15 12:46 gibson created 2014/10/17 10:23 gibson 2014/10/17 10:23 gibson 2014/10/17 10:22 gibson 2014/10/17 10:14 gibson 2014/10/17 09:44 gibson 2014/10/15 13:12 gibson 2014/10/15 13:04 gibson 2014/10/15 13:01 gibson 2014/10/15 12:55 gibson 2014/10/15 12:53 gibson 2014/10/15 12:53 gibson 2014/10/15 12:52 gibson 2014/10/15 12:46 gibson created Line 23: 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*} - Note that the difference between successive partial sums is a single term. + etc. 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}