fm and n are odd integers, then so is m · n.

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

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Q: Take any arbitrary integer n and then square it, which one is true? n2 cannot be in the form 7k + 5.…

A: Solution is given as follows :

Q: З and an - - 3ап-1 + an-2 for integers n>2. Evaluate and d4: Let a, = 2, a2

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Q: Show that 3 · 4n + 51 is divisible by 3 and 9 for all positive integers n.

A:

Q: the fourth power of an integer is x, and x is between 100 and 600. What is x?

A: It is given that the fourth power of an integer is x.That is, x = n^4, where n is a positive…

Q: If a is an even positive integer and b is an odd positive integer, then which of the following…

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Q: Let P = (4, 1, a), Q = (-2, 0, b) and v=i − 3j + 4k be two points and a vector in R³ respectively.…

A: The given points are 4,1,a and -2,0,b. The given vector is v=i-3j+4k in ℝ3.   The vector equation of…

Q: The value of (1 - i)24 is /2)24 6in O 212 O (2)24 -212 o None

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Q: Show that if n is any integer, then 3 divides n3 − n

A: To prove:  if n is any integer, then 3 divides n3 − n. Concept used: Here we shall use the identity:…

Q: exp(ix())= 4k+1 2

A:

Q: . Verify the formula п(n + 1) 2 for n = 10, 50, and 100.

A: ∑x=1nx = n(n+1)2To verify the formula for n = 10, 50 and 100.

Q: If a is an even number, then a³ is an even number.

A: Here, We have given that (a) is an even number then we have to prove that (a3)  is also an even…

Q: "find A2, A−2, and A−k (where k is any integer) by inspection."

A: NOTE: Refresh your page if you can't see any equations. . use the diagonal matrix formula

Q: For any integer a, show that a²-a+7 ends in one of the digits 3, 7, or 9.

A: For any integer a , we have to show that a2 - a + 7 ends in one of the digits 3 , 7 , or 9 . Note…

Q: se indirect proof to show that, "If n is an integer and 3n + 2 is even, then n is even

A: Let us solve the classical algebra problem in the next step.

Q: Suppose “a” is an integer. If 5|2a, then 5|a.

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Q: Show that 3 · 4n + 51 is divisible by 3 and 9 for all positive integers n.

A: Given , 3.4n+51 is divisible by 3 and 9 for all positive integers n''-1The statement 1 can be…

Q: #5 Find An if n is a positive integer and A = 4 -3 - 2

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Q: What is the prime number that's one-half the product of the only two consecutive prime numbers? 1 BO…

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Q: The S.D. of the first n odd integers is √85 , find n

A: Sum of first n odd numbers is given by: ∑ixi=n2 Sum squares of first n odd numbers is given by:…

Q: 4. Rewrite each expression so that each term is in the form kx", where k is a real number, x is a…

A: We have to rewrite the given expression in the form of kxn. Before going to simplify expression,…

Q: 10. Choose te bes The number, so that =zis called the logarithm of z.

A: Given : by=x

Q: where did the 26 and 10 come from?

A: where did the 26 and 10 come from?

Q: dim(M23) = O 3 O2 O 5 O None

A: We need to tell the dimension of vector space M23  This can be done as follows:

Q: 2 ) + ("**) = n²- .2 2

A:

Q: Let x and y be positive integers. When is x + y3 a prime number? When is x+y a composite number?…

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Q: 3 2z²+ +3x²-22x-61 - 12 2 र e da

A: Some of the properties of integration  ∫1xdx=lnx+C∫xndx=xn+1n+1+C∫af(x)+bg(x)dx=a∫f(x)dx+b∫g(x)dx