ltxprimer-1.0

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VIII .4. M ATHEMATICS MISCELLANY

Euler not only proved that the series $\sum_{n=1}ˆ\infty\frac{1}{nˆ2}$ converges, but also that \begin{equation*} \sum_{n=1}ˆ\infty\frac{1}{nˆ2}=\frac{\piˆ2}{6} \end{equation*} gives the output Euler not only proved that the series P ∞ n = 1 1 n 2 converges, but also that ∞ X n = 1 1 n 2 = π 2 6

Note that in display, the sum symbol is larger and the limits are put at the bottom and top (instead of at the sides,which is usually the case for subscripts and superscripts). If you want the same type of symbol (size, limits and all) in text also, simply change the line

$\sum_{n=1}ˆ\infty\frac{1}{nˆ2}$ to

$\displaystyle\sum_{n=1}ˆ\infty\frac{1}{nˆ2}$ and you will get

∞ X n = 1

1 n 2

Euler not only proved that the series

converges, but also that

∞ X n = 1

π 2 6

1 n 2 =

(Note that this also changes the size of the fraction. What would you do to keep it small?) On the other hand, to make the displayed operator the same as in the text, add the command \textstyle before the \sum within the equation. What if you only want to change the position of the limits but not the size of the operator in text? Then change the command $\sum_{n=1}ˆ\infty \frac{1}{nˆ2}$ to $\sum_\limits{n=1}ˆ\infty\frac{1}{nˆ2}$ and this will produce the output given below. Euler not only proved that the series ∞ P n = 1 1 n 2 converges, but also that ∞ X n = 1 1 n 2 = π 2 6 On the other hand, if you want side-set limits in display type \nolimits after the \sum within the equation as in Euler not only proved that the series $\sum_{n=1}ˆ\infty\frac{1}{nˆ2}$ converges, but also that \begin{equation*} \sum\nolimits_{n=1}ˆ\infty\frac{1}{nˆ2}=\frac{\piˆ2}{6} \end{equation*} which gives