If the coefficient of 4 consecutive terms in the expansion of (1+x)" are a₁, a2, a3, a4 respectively, then show that: 2a3 a1 a3 a₁ + a2 a3 + a4 a2 + = + a3

Q: 6[5+2(9-4)]

A: Consider the given expression.

Q: Find each (n+3)(n+2) (4n 5)(3n + 2) (n+7)(n + 5)

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: Write the binomial expansion for (x+ 2y)*. (x + 2y)* =D

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Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

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Q: How may elements are in the set [-2, 2] \N?

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Q: Find a, b, and n in the expansion of (a + b)" if the first three terms of the expansion are 729,…

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Q: Construct the seventh and eighth rows of Pascal’s tri-angle and write the binomial expansions of (x…

A: Pascals triangle: 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 1

Q: 4 a) (x² + b) (- x*)*

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Q: n (x - 1)" The sixth term of the expansion of x is 1287 8 X 3125 . Determine n.

A: Let us consider the expression a+bn. The binomial expansion of the given expression is , a+bn=C0n…

Q: Write out the full expansion of (x + y)^7 using either binomial coefficients or Pascal’s Triangle to…

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Q: How many pairs of integers (a,b) exists such that the product of a,b and HCF of (a,b) is 1080??

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Q: Use the binomial theorem to show that 72 Σ(1) ( **(?). i-0 0.

A: Use binomial theorem to show that given formula.

Q: Evaluate the following * [: 2x(4x² – 3)³dx (4x²-3)6 +C 24 O (4x² - 3)-6 24 +C (4x²-3)6 24 O " (4x² -…

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Q: -1- 3 5

A: Topic = Algebra

Q: Show that n-lis divisible by 8, if n is an odd positive integer

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Q: Write the first 3 terms of the expansion of (3x - ) – 2)" and simplify |

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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

Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: 7)-2abc * 4a²bc+

A: We will find the product.

Q: How many zeroes does 188! end with?

A: count number of five's in 188, 5*2=10 . Divide 188 and write quotient again divide quotient again by…

Q: write out the correct expansion for (a+b)^4

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Q: The fourth term in the expansion (2r + y)' is

A: The equation for the combinations n taken r at a time is equal to Crn=n!n-r!r!.  The continued…

Q: √ (2x - 7)6 12 (2x + 7)- 12 (2x - 7)5 + C + C (2x - 7)-6 12 (2x + 7)6 12 - + C - + C

A: Topic = Integration