'п-2y (k-2) Problem 2. Consider the identity k(k – 1)(") = n(n – 1) () (a) Give an algebraic proof of the identity. (b)' Give a combinatorial proof of the identity.

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A: Explanation of the answer is as follows

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A: Given: Objective: To write the above formula in MATLAB.

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Q: (d) Using Fermat's theorem, compute the remainder of 8103 when divided by 13

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A: We have explain the property of identity matrix.

Q: 0 (HINT: First move terms around so that all terns are positive)

A: To prove:             ∑k = 0n(-1)k nk = 0

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Q: Using Fermat's theorem, compute the remainder of 8103 when divided by 13

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Q: (2) Prove that (1+x)" > 1+nx for all x > 0 and n > 1.

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A: (iv) Show that H∧H' entails H'.

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