query: Manipulation of Power Series
positive_passages.docid: 24108
positive_passages.text: Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$
negative_passages.docid: 155367
negative_passages.text: summation of multiplying series with negative terms
negative_passages.docid: 101011
negative_passages.text: An intriguing relation between two alternating series
negative_passages.docid: 76311
negative_passages.text: $f'' + f =0$: finding $f$ using power series
negative_passages.docid: 63985
negative_passages.text: Evaluating series using operator
negative_passages.docid: 69270
negative_passages.text: Questions about the powerseries $\sum_{n=0}^{\infty}\frac{1}{n^d}z^n,d\in\mathbb{R},z\in\mathbb{C}$
negative_passages.docid: 151477
negative_passages.text: computing the series $\sum_{n=1}^\infty \frac{1}{n^2 2^n}$
negative_passages.docid: 75529
negative_passages.text: Series prove or disprove statement
negative_passages.docid: 72427
negative_passages.text: Series expansion for small ratio of variables
negative_passages.docid: 145390
negative_passages.text: Formal power series ring, norm.
negative_passages.docid: 45101
negative_passages.text: Convergence of Power Series with $z^{2^k}$
negative_passages.docid: 76387
negative_passages.text: Evaluate the series $\sum_{n=1}^{\infty} \frac{2^{[\sqrt{n}]}+2^{-[\sqrt{n}]}}{2^n}$
negative_passages.docid: 143756
negative_passages.text: Introduction to Analysis: Multiplication Theorem for Series
negative_passages.docid: 124217
negative_passages.text: Can there be more than one power series expansion for a function.
negative_passages.docid: 13035
negative_passages.text: The set of functions which map convergent series to convergent series
negative_passages.docid: 56007
negative_passages.text: Does this tricky series converge?
negative_passages.docid: 120714
negative_passages.text: find the radius of convergence of the following power series