() - (" ;')-(,".) Show that: n+1

Q: Prove that (-1ti3)" + (-1-is3)" has either the value 2n+' or the value -2" if r is any ). integer…

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Q: Which of the following is false? O ("2) = 2(") k ㅇ ") %3 (4") + (F) k n(n+1) (":"): 2 2 O ()² = (?)…

A: We have to check whether given statement is true or false.

Q: Compute the following: (a) 4!, (b) (), (c) (₂), (d) (), (e) (7), (f) (2)-(2) where n is a…

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Q: Proved Ax (BNC) = (AX B)n (AXC) %3D

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Q: Show for all natural numbers n >= 3 that [(1 + (1/n))^n] < n.

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Q: 11. (a) What does the symbol n! mean? Find 5!. (b) Define (), and find (2).

A: To find 5! and to find the value of 52

Q: Prove a^2 +4a+3 is odd if and only if a is even.

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Q: Show the following for [im 11x|lp = 11x11.00 P-0 XER

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Q: In 3 - In x - In(x + 5) = 0

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Q: Compute: [2 1 0 5 - ] [ ] -5 ܗ

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Q: Show that n := e2™i/n is a primitive nth root of unity in C. Verify that (S3 - )? = -3 in C. Verify…

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Q: How many zeroes are at the end of 1000!/(500!500!)?

A: Calculate number of zeroes in 1000! and then subtract it from the number of zeroes in (500!500!).

Q: Prove that if x is an even integer, thenx^2−6x+ 3is odd

A: Any integer of the form 2m+1 is odd.

Q: п(п + 1) Show that , k 2 k=1

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Q: Give a combinatorial proof for the identity 1+2+3+..+n= (",").

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Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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Q: (-5) + 4 – 1+ 4- (-21) * (-7)) ova

A: Simplification

Q: Prove that n-5 is odd iff n^2-1 is odd

A: Please check step 2 for the solution.

Q: Prove that 2^? +3^? is a multiple of 5 for all odd ?∈N.

A: We will solve this problem using principle of mathematical induction.

Q: prove the following using either direct or indirect proof  a. if a is an odd integer, then…

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Q: Assume that n ∈ N. Prove that if 3|(2n + 1) then 9|(10n^ 2 + n − 2).

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Q: Show that |x^n| = |x| ^n for every positive integer n and every real number x.

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Q: Let (x) = -7x* + 3x² a) A-x) = ? 2. b) Ax) = ? c) Which is (x) : even, odd, or neither ? Why?

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Q: and

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Q: Determine the value of f(ln 2) when ƒ'(x) 4eª +e-, ƒ (0) 1. 2. 3. = 5. f(ln 2) f(ln 2) f(ln 2) =…

A: f'(x)=4ex+e-xgiven f(0)=3we know  (i) ∫exdx=ex+c(ii)  elnx=x

Q: Suppose A = {2, 5, 7, 9, 13, 25, 26}. (a) Find n(A).

A: