2 years ago

Can anyone help? I’d greatly appreciate it :)

Mathematics

1 answer:

Lena [83]2 years ago

8 0

Answer:

bilmiyorum sna kolu gelsın

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Step-by-step explanation:

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This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

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$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

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$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

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$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

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3 years ago

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