Category:Power Series Expansion for Reciprocal of Square Root of 1 - x
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This category contains pages concerning Power Series Expansion for $\dfrac 1 {\sqrt {1 - x} }$:
Let $x \in \R$ such that $-1 < x \le 1$.
Then:
| \(\ds \dfrac 1 {\sqrt {1 - x} }\) | \(=\) | \(\ds \sum_{k \mathop = 0}^\infty \frac {\paren {2 k}!} {\paren {2^k k!}^2} x^k\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1 + \frac 1 2 x + \frac {1 \times 3} {2 \times 4} x^2 + \frac {1 \times 3 \times 5} {2 \times 4 \times 6} x^3 + \cdots\) |
Pages in category "Power Series Expansion for Reciprocal of Square Root of 1 - x"
The following 3 pages are in this category, out of 3 total.