Show that the middle term in the expansion of (1 + x)2¹ is (1-3.5 (2n- -1)) 2"x", where n is a positive integer. n! ...

Q: Sam baked 6 cupcakes less than Michelle. Sam baked 18 cupcakes. Which equation will tell you how…

A:

Q: Find the constant term in the expansion (2y + 1) O 4032 4232 O 4323 4023

A:

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

A:

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

A:

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: . (a) Find the coefficient of r in the expansion of ‹ (² + ²)² (+ -)

A:

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

A:

Q: Зх —1 A B (b) (i) Express (1– x)(2 - 3x) in the form - x 2-3x , where A and B are integers. Зх— 1…

A:

Q: for

A:

Q: Consider the expansion of (2+x²³²) ¹+¹ ² where 2+2 nt next the coefficient of X² is 1792, Given that…

A:

Q: Prove the following using the binomial theorem: ()=()+ 2n

A: In this context, the aim is to prove 2n2=2n2+n2.

Q: Compute the coefficent of x8    in the expansion of (3x -2)13

A: The given expression is,

Q: 3 O Find the first three terms of the expansion of (1+x)(2x-1)

A: The given series is 3(x+1)(2x-1) We have to find first three terms of the given series. This can be…

Q: 16. Find the term containing x18 in the binomial expansion of (x2- y)15.

A: A binomial expression is an expression of the form a+bn. This binomial expression can be expanded…

Q: (x³ + })*

A:

Q: Show that 2n is O(3n) but not that 3n is not O(2n)

A: We need to show that 2n is O3n but 3n is not O2n Definition of Big O notation: Let f be a real…