4. Let bo = 1, b1 = 3, and for cach integer k> 2, we have bz = 4bg–1 - 4bg-2 Prove that for all integers n>0 we have that bn = 2" (1 + 5) %3D

Q: Let A = 0 -5 1 C. A-1 a. det (A) b. 7A + 5I = || d. AB = - 2 - 3 0 = e. BT AT = -5 1 – 1. and B = 16…

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Q: solve 5.3 (using k(pi-k)/2) and setting k =pi/2 or by your own methods if you have easier ones

A: It is known to us that

Q: 7. Prove that if a, = 1, a1 = 4, and a, = 6a,-1 – 9an-2 for n > 2, then a, = 3"-(3 + n) for all n 2…

A: We have to prove the following result by using the principle of mathematical induction.

Q: Prove that if n is an integer and 3n+2 is even, then n is even using a proof by contradiction. Rank…

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Q: Σ1 (−1) = (n+1)(-1)", 2

A: We have to prove  Prove that ∑ni=1 i2(−1)i = ((n+1)(−1)nn)/2 , where n is a positive integer. We…

Q: Compute Pearson's r demonminator with the computational formula and use 4 decimal places for all…

A: We have given that data  stress : exam scores:  5             4 6               5 6             2 4…

Q: Find a closed formula for a, if ak = 5n² + 4n k=1 an =

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Q: (11.1) Show that for any two positive integers m and n. m {m² + m + ¹} = {x{"+ *} m k k=0

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Q: 5 Find

A: To find the integral, first use the sum and difference rule and separate the integral.…

Q: 4. Prove that 3i² + i = n(n+ 1)?

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Q: QUESTION 3 Let P(x) is cold Q(x,y)=xisy. The universe of x is seasons, and the universe of y is…

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Q: Show that det [1 1 0 0 1 1 0 0 1 0... 0 0 1 ⠀ ... 0000 1000... 00 00 11 0 1 = 1+ (-1)"+¹.

A: As per the question we are given a matrix determinant, whose all diagonal and super-diagonal…

Q: Indicate the smallest integer n such that (6x²+4x)³ f(x) = € 0(x¹). 2A-4x On=4 O n=2 O n=1 O n=6 O…

A: f(x) = (6x2 + 4x)3/(x4 - 4x)         = {2x(3x + 2)}3/{x(x3 - 4)}        = 8x3(3x + 2)3/{x(x3 - 4)}…

Q: Let a and b be positive integers with ged(a, b) = 1. Show that if d > ab, then as + tb = d has a…

A: 4. Given that a and b be positive integers with gcd(a, b)=1.     To prove that if then has a…

Q: Find SU U. 10 9. *+6 x+10 S

A: We have to find length of secent US.

Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

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Q: Problem 1. Let M = 14 -5 −1 9] 10 Find formulas for the entries of M", where n is a positive…

A: The given problem is to find the matrix Mn for the given following matrix M. We have to find the…

Q: Let v= (4,1). Carry out the following computation. Find -7v. |- 7v| = D %3D

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Q: Prove that (1,1) is an element of largest order in Zn1 + Zn2. State the general case.…

A: We know that order of any group G×H is lcm(|G|, |H|)     |G| = order of group G. Similar for H. Now,…

Q: Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we…

A: Decomposing Unit FractionsThe problem of decomposing a unit fraction as the sum of two other unit…

Q: Example 9.7.1 showed that the following statement is true: For each integer n2 2, n(n – 1) („-2) -…

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