2n Using the expansion of (1 + x)² and given that 2nC₁ + 2(²nC₂) + 3(2n C3) + ... + 2n(2nC₂n) + 2n(²¹℃₂n) = n × 2²n Show that 2(²nC₁) + 3(²nC₂) + 4(²″C3) + ... + (2n + 1)(²nC₂n) = (n + 1) × 2²″ − 1

Q: Find the Taylor series generated by f at x = a. f(x): %3D —, а %3D3 a =

A: Given function fx=1x. To find the Taylor series generated by f at x = a, where a = 3.

Q: 5ェ 4°(1- 等+ 5ェ +...)

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Q: 10. Let [ A= 103 -1 21 02 Calculate det (A) by cofactor expansion.

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Q: Using the binomial expansion n (1 + x)² = ± (1) x², k=0 prove the following relations n n…

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Q: (7) Use congruences to prove the following. They were proven by induction in Prob- lem 19 in Section…

A: (a) To prove that 9 divides (4^n+15n-1), we need to show that (4^n+15n-1) is congruent to 0 mod 9.…

Q: 26 E(- 1)"2n - %3D n=0

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Q: a/2 2. Evaluate f[(e)i-2sin(t) j+3cos(1)k]dt

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Q: Find the Taylor series generated by f at x= a. f(x) = -, 1 a = 3 X (x- 3)" Ο Α Σ 3" OA. n =0 (x –…

A: We have to find the Taylor's series for given function at a=3 . For this all order derivatives of f…

Q: Use the binomial theorem to expand the following: (a) (x + 2y)* (c) (3x + 1)4 (b) (x - y)6 (d) (x +…

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Q: Prove. Show all steps to get to ln (2^(-2n))

A: Step 1: Given data :The expression is represented as, ln(BA​)=ln(((2N)![(N−n)!]2)(N!)2(2N−n)!​).…

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Q: 21) f(x)=47x A) (4 ln 7)47x Write summation notation for B) (7ln 4)47x x(In 2) C) (In 4) 47x x(In x)…

A: Finding the derivative of f(x)

Q: The principal at x=o of f(x) = √₂² +2² - x - x² (with respect to up(x) = x) is: (c) x8/7-x² (d)=x²…

A: To find the principal part of the given function  as with respect to g(x)=x, we will use the…

Q: (4x*) for all x#0? Show the manipulations that lead to your 5. Which of the following is equivalent…

A: Explanation of the answer is as follows