(a) (b) Find the limit of the following sequences or show why they diverge. In(5n6) 1 7n-1 +n8 8n³ + 2n +9 3n - 4n³

Q: 1) (a) Determine the simplest form of the expansion of (2x4 - 1) 4. 4x (b) Determine the coefficient…

A: Consider,(1) (a) Given,(2x4−4x1​)4use the binomial theorem formula to simplify the given…

Q: Given that the 4th term in the expansion of 2+x has the 3 8 maximum numerical value. Find the range…

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Q: limn0 In(2n-3) -) is 8. n+5 Select one: 2 non of them

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

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Q: Prove that each of the following sequences diverges: (a) {4n - 5} (b) {√3n+1} n² + 71 8n +3 (Hint:…

A: We know if a sequence is unbounded the it is divergent.

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

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Q: Sp-3 2x If there are 23 terms in the expansion of ху then the value of p is

A: We will find out the required value of p.

Q: (2) Show that each of the following sequences (an) in R is convergent, and determine limn- an: n² +n…

A: According to guidelines we can do only first three sub parts.. thank you A sequence is said to be…

Q: Which one of the sequences below is divergent? 2n? 3n + 17 2n 3n + 5J 2n n +n +1 D {2-} D

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Q: i. Find the coefficient of x in the expansion of ( 2x –÷) . ii. Hence find the coefficient of x in…

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Q: 3. (a) Find a closed formula for the generating function A(z) of the sequence an (3n-7) (-2)".

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

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

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Q: Evalu

A: (a)

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

A: Explained below

Q: In the following list, select all the correct expressions if G(x) is the generating function of the…

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Q: (c) Find the term independent of x in the expansion of, 15 2 +

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Q: 3. Write the first four terms of the expansion of the following functions In (1-2r) (b) 1+

A: write the first four terms of the expansion of the following functions 1) fx=ln1-2x1+x…

Q: Find the limit of the sequence {(₁+ 3 n+ 5 2n S

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Q: 2. (a) Given that (2 + x)" (1-x)" =+ pa³+qx²+7x+s, determine the values of P.4.9, and s. (b) Without…

A: Step 1: Step 2: Step 3: Step 4: