a) Using the Difference Taylor Theorem find the constants ao, a1, a2, 03 such that *-- () - - () -- () +() + a1 + a2 + a3 b) Use your answer in (a) and the Hockey Stick Identity to find an explicit formula for 1*+2* +3* +• · ·+n*. Leave the answer as a linear combination of binomials.

Q: Q2/ Fin x in the

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Q: (15) Let a, b = Z. Prove that if a is divisible by 4 and b is divisible by 4, then: (a) ab is…

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Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

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Q: 2021 2. Expand (1 + v3i)“ recall the binomial theorem.

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Q: (x³ + })*

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Q: 3. Use the binomial theorem to prove that 2n 2n |22n–2k = (2.5)2". k k=0

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Q: Find a formula for the general term a, {5, 8, 11, 14, 17, .} 5n + 3 On+3 O 3n + 2 O 2n + 3

A: We can answer the question as below

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Q: (b) Prove that E-o(-1)* )= 0 for all positive integers m.

A: We have to prove ∑k=0n-1kkn=0 for all positive integer n