Using mathematical induction, show your solutions to prove that  1 + 5 + 9 + ... + (4n-3) = 2n^2 - n.

Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate ?(x)

A: given , expression :- 32x+7 we have to prove that given expression is divisible by 4 .

Q: 78 (5y + 2)

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Q: What is the result of 1+1?

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Q: how does the a in the second row become a 0

A: It is given that the row operations are performed on matrices as, 010-10a0-a0~01a-10a000~-10a010000…

Q: Express 2x-1/2x-5 in the form p+ q/2x-5

A: Given expression is 2x-12x-5

Q: find (2n +1)! = 120

A: Here we have to find the value of n.  2n+1!=120

Q: 22n+1 3n+1 2.

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Q: =n* + 2

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Q: Choose the property of addition that j (6+a)+5=6+(a+5)

A: The given addition 6+a+5=6+a+5. We have to find the property of addition that represents the given…

Q: Determine the Fourier Series of the function f(x)= |x|, -3 ≤ x ≤ 3, f(x) = f(x+6).

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Q: Determine whether the statement is true or false. 9<-3 Is the given statement true or false? False…

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Q: 2х (b) 2 +1)

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Q: Find the 4th term ( 2x + 3)4

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Q: Show that 14C5 x 5! = 14P,. %3D

A: Combination formula:Crn=n!r!(n-r)!Permutation formula:Prn=n!(n-r)!

Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: polyhomial iS equivalent t0 2n + 5)²? O 4n? + 25 O -4n? + 25 O 4n? - 20m + 25 O -4n? - 20n + 25

A: Given,  A polynomial  -2n+52  We have to find the polynomial equivalent to -2n+52

Q: What is the conjugate of 3 + √5

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Q: A = D −13 ๆๆ || 4 B = -2 0 1 4 3 1 -2 = 0 -4 3 -4 5 " 3|N NN M 916 | | NO

A: Given:  A=13-43-2014, B=-32725216133116, D=31-250-4-453 To Find: The value of D+AB

Q: Find the 3rd term  (5 -3x)5

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Q: Find the 4th term in the expansion of (2x - y)6. Explain the thought process leading to the answer

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Q: Find n, if 3n+18=0

A: Linear equation question

Q: When multiplied out, what are the first 4 terms of (2x + y)10 ? Show all work.

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Q: Q1/ Using binomial formula to expand (-2+B)5 .

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