Would anyone have any idea on how this is done? Truly puzzled at this point :P
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J.Khelly
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Where is this question from? – Joppy Sep 27 '17 at 09:17
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It's a practice problem assigned by my university professor. – J.Khelly Sep 27 '17 at 09:19
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Here's a MathJax tutorial :) – Shaun Sep 27 '17 at 09:41
1 Answers
2
- $a_0 = 2$
- $a_1 = 2\sqrt2 = 2 \dfrac{\sqrt2}{1}$
- $a_2 = \sqrt2(\sqrt2-1) = 2 \dfrac{\sqrt2(\sqrt2-1)}{1 \cdot 2}$
- $a_3 = \dfrac13\sqrt2(\sqrt2-1)(\sqrt2-2) = 2 \dfrac{\sqrt2(\sqrt2-1)(\sqrt2-2)}{1 \cdot 2 \cdot 3}$
$$\begin{array}{rcl} a_n = 2\dbinom{\sqrt 2}{n} \\ f(x) = \displaystyle \sum_{n=0}^{\infty} 2\dbinom{\sqrt 2}{n} x^n \\ f(x) = \displaystyle 2 \sum_{n=0}^{\infty} \dbinom{\sqrt 2}{n} x^n \\ f(x) = \displaystyle 2 (1+x)^{\sqrt2} \\ \end{array}$$
Kenny Lau
- 25,049