- #1
Dickfore
- 2,987
- 5
These identities might be considered as true:
[tex]
\begin{array}{rcl}
1 - 1 + 1 - 1 + \cdots & = & \frac{1}{2} \\
1 - 2 + 3 - 4 + \cdots & = & \frac{1}{4} \\
1 - 4 + 9 - 16 + \cdots & = & 0 \\
1 + 1 + 1 + 1 + \cdots & = & -\frac{1}{2} \\
1 + 2 + 3 + 4 + \cdots & = & -\frac{1}{12} \\
1 + 4 + 9 + 16 + \cdots & = & 0
\end{array}
[/tex]
[tex]
\begin{array}{rcl}
1 - 1 + 1 - 1 + \cdots & = & \frac{1}{2} \\
1 - 2 + 3 - 4 + \cdots & = & \frac{1}{4} \\
1 - 4 + 9 - 16 + \cdots & = & 0 \\
1 + 1 + 1 + 1 + \cdots & = & -\frac{1}{2} \\
1 + 2 + 3 + 4 + \cdots & = & -\frac{1}{12} \\
1 + 4 + 9 + 16 + \cdots & = & 0
\end{array}
[/tex]