By taking the antiderivative of the binomial expansion, prove the following: + 1² ( 1 ) + 1² (2) 2 1+ +...+ 1 n+1 N n = 2n+1 -1 n+1

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: Determine the coefficient of x3 in the binomial expansion of (1 + 5x)½ by completing the given…

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Q: Which of the following real number would be the coefficient of x in the binomial expansion of

A: Using binomial expansion formula find that there is no term of x in the binomial expansion of the…

Q: (a) Find the binomial expansion of (1 – x)-1 up to and including the term in x?.

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Q: Find the specified nth term in the expansion of the binomial. (x − 7y)5,    n = 3

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Q: a. Coefficient of x1/y21 in the expansion of (3x-2y)38 b. Coefficient of x23y41 in the expansion of…

A: The expression, nr can be defined by the formula, nr=n!(n-r)! r! .

Q: Find the indicated terms in the expansion of the given binomial. The last two terms in the expansion…

A: Here given binomial,

Q: (c) Find the term independent of x in the expansion of, 15 + 4x?

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

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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: Determine the coefficient, a, for the term shown in the binomial expansion of below term : ax³y7…

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Q: P1. In the binomial expansion of (2-3) written in terms of descending power of X, find; a the th…

A: Explained below

Q: Use the Binomial Theorem to prove that 4 (¹ + 5)^² 5n 53 25 8 25n' for n ≥ 1.

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Q: п n 9. Using the Binomial Theorem, show that Σ = n 2"-1. k k=0

A: We need to show that- ∑k=0nknk = n2n-1

Q: The probability that an archer hits the target is p = 0.9, so the probability that he misses the…

A: Here's it follows binomial distribution with trial 6 and probability of success 0.9 , probability of…