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I have one question. Is it true?

[tex]\sum^{\infty}_{k=0}a_kx^k=\sum^n_{k=0}a_{n-k}x^{n-k}[/tex]

I saw in one book relation

[tex]\sum^{\infty}_{k=0}\frac{(2k)!}{2^{2k}(k!)^2}(2xt-t^2)^k=\sum^{n}_{k=0}\frac{(2(n-k))!}{2^{2(n-k)}((n-k)!)^2}(2xt-t^2)^{n-k}[/tex]

Can you give me some explanation for this step?

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# Infinite sum question

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