Question 4 For any integer k > 0 and any integer j, we can define () j-(j–1).(j-k+1) k! (Notice what һаppens when j < k!!) You саn assume that Pascal's identity holds for this extended version of the binomial coefficients. Prove that -o (2) = (*)- j=0 \k+1)

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Q: (18)280 mod 125 =

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Q: (2) Give a proof by contradiction of theorem “If n^2+1is odd, then n is even”

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A: We know the binomial therom expansion

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.