2. Use the Binomial Theorem to find the coefficient of x2000 in the expansion of (3x – 7)2021. 3. Use the Binomial Theorem to prove that 2* . (:) = 3". k=0 Now find a double-counting proof of this identity (hint: double count strings of length n from an alphabet {a, b, c}. Group these words by the number of entries that are not the letter a.)

Q: In the expansion of (2 + 4y?) a. How many terms are in the expansion after like terms have been…

A: We will find the answers of all parts using binomial expansion.

Q: 17. Expand using Pascal's Triangle or the Binomial Theorem. Be sure to show the setup. Then,…

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Q: What are the first and last terms in the expansion of (5x + 4y)*?

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Q: Find the coefficient of a-2 in the binomial expansion of  (27a2 - (1/81a3))9

A: Let us consider the expansion x+yn The binomial expansion is obtained as x+yn=∑k=0nCknxn-kyn

Q: Identify the expression of x for which the following equation holds for every positive integers n…

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Q: 1. Use the binomial theorem to fully expand (x² - 2y)4. Expectations Each term of the full expansion…

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Q: Use the binomial theorem to expand the expression (u - 5v)¹

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Q: Use Pascal's Triangle to expand the binomial (x + 1)° O 25 + 5x4 + 10x + 10x2 + 5x + 1 O g5 - 5x1-…

A: Pascal's triangle…

Q: 2. Determine the value of (k) in each of the terms below from the binomial expansion of 15 (a + b)…

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Q: obtain the binomial expansion of (1-2x)^5 and use it to evaluate(0.98)^5 correct to 5d.p

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Q: 1. How many terms are in the binomial expansion of (x + y²)14? correct number of terms)

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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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