Drag each tile to the table to multiply (6x-y)(2x-y+2)

Mathematics

1 answer:

77julia77 [94]3 years ago

7 0

The other answer is 12x2 – 8xy + 12x + y2 – 2<span>y</span><span />

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If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

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Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

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$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

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$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

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