Use the binomial theorem to show that for all integers n 2 1, 3" = (6) + 2 (4) + 2° (") -

Q: n -r Prove that („",) : r+1

A: Combinations: Combination is the selection of n items taken r at a time is

Q: Suppose r is a non-negative real number and n is a natural number. Use the Binomial Theorem to prove…

A: The binomial theorem states that for the positive integer value n: x+yn=∑k=0nCknxk+yn-k

Q: 1. In your own words, what is the binomial theorem. Find the 5th term of (x+7)

A: Given : x+77

Q: Expand 3x + 2y)7 using the binomial theorem. Simplify your final result.

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Q: (1+ 2x + 4x? +8x + ...)(3x² + 3x* + 3a° + · . .)(x³ + 2a® + 3x° +

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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: Find a formula for ¹ - 1²/ (²1) + 1² ( 2 ) -—- ... ₁ (2). (G) + (-) + I u

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Q: Use the Binomial Theorem to show that 50 E)(-2)" = 1. %3D

A: Binomial Theorem:

Q: 10. Use the binomial theorem to evaluate (2r³ - y) 5.

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Q: Expand in binomial theorem (2x-y)7

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Q: 4. Find the expansion of (x + y)6 using Binomial Theorem.

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Q: Write down the expansion of : 4 1 3x 2 by the binomial theorem.

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Q: Using mathematical induction, prove that the Binomial formula holds for complex numbers (²1 Ĺ (2₁…

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Q: Write the binomial expansion for (x+3)°. ..... (x + 3)° =D

A: Solution...

Q: The third term of the (x-3y)5 of the following binomial is:

A:

Q: 9. (a) Using Pascal's triangle, expand and simplify (1 + 2)- (1-2.r)". (b) Using the binomial…

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Q: Find a formula for ¹ - 1²/ ( 7 ) + 3² ( 2 ) - ··· + + (−1)n. 2+1(1).

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

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

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Q: 4.-Use the binomial theorem to find the first four terms of development 1 (4 + x)2

A: We have to find the first four terms of the expression (4+x)−12, we'll first rewrite it…

Q: Which one of the following is a first degree binomial

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Q: Use the Binomial Theorem to find the coefficient of x' in the expansion of (x+3)" ...-.

A: on using binomial theorem we get the coefficient of x^7 that is

Q: Which of the following is the value of the coefficient y on the right side of the equation given…

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Q: (x³ + })*

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Q: The sum of the entries in the nth row of Pascal's triangle is equal to 2"1 for each n e N. Proof:…

A: Here we will check whether given statement is true or false,

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

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Q: 3x2 Q1/ A/ Expand with binomial formula: (1- * Q1/B/ Find the value of G? -15 3- 36 = [4 -6 4 -13 -4…

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Q: Using the binomial theorem to find the 4th term of √x + 2

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Q: Find the middle term in the binomial expansion of(x-3)".

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Q: Give a combinatorial proof for the identity 1+2+3+..+n= (",").

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Q: (Vx - V3)° 6.

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Q: 10. By Binomial Theorem (2a – b)* =16a* – 32a’b+24a*b? – 8ab³ +b* | a. TRUE. b. FALSE.

A: We know the binomial therom expansion