Use mathematical induction to divisible by 5 for all nt Ni int: Use the binomial formula: (a+b)² = 0² +50² b + 100³b² + 100²6²³² +5064 +65 prove that n²³-n is.

Q: If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion…

A: As given above that n be a positive integer. And the given expression is: 3x-2yn We have to prove…

Q: Using a binomial approach, find the sum S given by n+1 S="C₁ + "+¹C₁ + "+2² C₂+...+ "*C,

A: Here we can use the following formula to find the sum nCr+nCr+1=n+1Cr+1and nC0=1

Q: Instruction: Use extra paper for the computation and fill up all the blank based on the value that…

A: Given:         2a-b25 Using binomial theorem: The expansion is given by the following formula:…

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: Which is the correct expansion of (x+4y)^3 using the binomial theorem?

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

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

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Q: 1. Use the binomial theorem to expand (a) (1+x)* and (b) (1+x). 2. Use the binomial theorem to…

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Q: use tge binomial formula to find the coefficient of the q24z term in the expansion of (q-3z)25

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Q: Use the binomial theorem to expand the following expression. (u – v)5 By the binomial theorem with 5…

A: Given expression (u-v)5 Using binomial theorem,

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

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Q: Find the sum of coefficients in the expansion (2x+1)^3 (x+2y)^4. 2610 2817 2187 2160

A: We can solve the problem by expanding this and adding them

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: Use the Binomial Theorem to expand: (x- 2y)* a. x* - 8x*y + 24x²y² – 32xy + 16y* b. x* - 16y* c. x*…

A: Expandx−2y4

Q: Find the binomial expansion of (1+0.05)1/2 Show each step

A: The binomial expansion is given below_

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

A: Use binomial theorem to show that given formula.

Q: Find the tenth term in the expansion (x+3) 2? Select one:

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Q: Use the first 3 terms in the expansion of (2+5x)6 to approximate the value of (2.05)6

A: We know that a+bn = C0nan-0b0 + C1nan-1b1 + … + Cnnan-nbn

Q: Find the indicated term of the binomial expansion. (√2₁² +1³); second term 3 u

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Q: Calculate the coefficient of 7 in the Binomial expansion of (x² + x−¹)¹7.

A: Given that x2+x-117  This is in the form x+an Here  x=x2  , a=x-1  and n=17   .

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: Use the Binomial Theorem to find the indicated coefficient or term. 13) The 3rd term in the…

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Q: Find an expression, in terms of n for the coefficient of x in the expansion (1+4x) + (1+4x)² +…

A: ANSWER :

Q: The second, third and fourth terms in the binomial expansion (x + a)" are 240, 720 and 1080,…

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Q: Find all positive integers n for which n1º +1 is divisible by 10.

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