As stated above, the series is:
1 + 2 - 3 + 4 - 5 + 6 - 7 + 8 - 9 + 10 - 11 + 12 - 13 + 14 - 15 . . . ± (n - 1) ∓ n
What would the sigma notation be for this series, starting at 1, ending at n?
Thank you very much for your time!
$\endgroup$3 Answers
$\begingroup$$$2+\sum_{k=1}^n (-1)^{k}\cdot k$$
$\endgroup$ 4 $\begingroup$A more abstruse solution: $$\sum_{k=1}^n (-1)^{k \cdot \textrm{sgn} (k-1)}k$$ where $\textrm {sgn}$ is the signum function.
$\endgroup$ $\begingroup$i think $$\sum_{k=1}^{n}(-1)^{k+\lfloor\frac{1}{k}\rfloor}\cdot k$$ works
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