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Mathematical Analysis Fundamentals by Agamirza Bashirov

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Proof

We will use the induction principle. Fix arbitrary a,bRimage and let the preceding equality be the assertion P(n)image. Then P(1)image is obviously true. Assume that P(n)image is true for some nimage. Then by Lemma 2.11,

(a+b)n+1=(a+b)k=0nn!k!(n-k)!an-kbk=k=0nn!k

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