Find a formula for an, n > 1, if an is given by

Q: Produce a simple formula for a where a, n € Z and 1 ≤ a ≤ n. i=a

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Q: 2. Find an explicit formula for аn 3 За,-1+ 10ар-2 and ao %3D 0, ај 3D 7 An where

A: The solution is given as

Q: Find the value of z if e =1.

A: Our Aim is to find the value of z if ez=1 -(i)

Q: For any n e N, let An = {x € R | –n <x < n}. Prove that NneN An = A1. (Recall that we define 0 ¢ N.)

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Q: Given n=35. x=13. Find out the value of y=? (all possible) such that (x*y) mod 35=1.?

A: We will use (13y)mod35=1 to find all possible values of y by writing given congruence in expanded…

Q: In (x) The numerical value of dr is equal to .......

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Q: For each n e N, let A, = (}, } + ) %3D Find Unen An. Find Nnen An.

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Q: Find the largest number δ such that if |x − 2| &lt; δ, then |5x − 10| &lt; ε, where ε = 1.

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Q: (as (4) = Solve for x on To, ZC)

A: we have to solve the following

Q: e 1 for sub

A: Solution of the problem as follows

Q: A culture of bacteria has an initial population of 330 bacteria and doubles every 8 hours. Using the…

A: Given equation is as below: Pt = P0.2tdhere P0=330t=17d=8

Q: (b). Find the value of z if e =1.

A: Solution: Consider the equation : ez = 1 Now, taking natural logarithm on both sides we have ln ez =…

Q: Find a number a + 5 such that S" (1 – æ) dæ = 0

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Q: M d formulas for the entries of M", where n is a positive integer.

A: To find the power of a matrix

Q: On what formula?

A: To determine: The formula required for any computation when a graph of a time series is given.

Q: Find the largest number ő such that if ]x – 4| < 6, then |2x – 8| < E, where e = 0.5. Repeat and…

A: x-4&lt;δ then 2x-8&lt;ε where, ε=0.5  2x-8&lt;0.5  2x-4&lt;0.5  2x-4&lt;0.5  x-4&lt;0.52…

Q: Find the largest number d such that if |x – 3| < 8, then |5x – 15| < ɛ, where ɛ = 1 Repeat and…

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Q: Evaluate the following formula for P₁ = 0.5, P2 = 0.1, P₁ P2 = 0, p=0.347407, q=0.802649, n₁ = 68,…

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Q: (b) Since the solution is unique, the resulting formula must agree with the answer to Exercise 9.…

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Q: Let a, b eR with a < b. Assume that a + <b - for all n e N. Show that n n=1

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Q: Using only a simple calculator, find the values of k such that det(M)=0, where M=⎣−1 k 0 1 1 k 1 1…

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Q: Compute the values of the following terms:

A: since u have asked multiple questions in a single request so we will be answering only first…

Q: Given the explicit formula, find the first 5 terms. f(n) = 3"-1 %3D

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Q: (b) Use the iteration formula 4(3-х,) (3+x,) with x, = 1 to find, to 2 decimal places, the value of…

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Q: The characteristic of Z5[x]/ 3 5 O O C

A: Introduction: The characteristics of a field is either 0 or prime. Suppose, a polynomial fx is…

Q: Express the given repeating decimal as a quotient of integers. If possible, reduce to lowest terms.…

A: Simplification

Q: Find the term independent of x (i.e. whenx in the following expansion : 1, i.e x") and its…

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Q: Find the largest number δ such that if |x − 4| &lt; δ, then |2x − 8| &lt; ε, where ε = 0.1.δ ≤ 1…

A: When ε=0.1 and δ≤1Simplifying the absolute value inequality:

Q: Apply Bessel's formula to find the value of f(27.5) from the table: X: 25 26 27 28 29 30 f(X):…

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Q: A culture of bacteria has an initial population of 620 bacteria and doubles every 2 hours. Using the…

A: Initial population of bacteria was 620. It doubles every 2 hours. We have to calculate the…

Q: For the given value of n, find all the units in Zn.   n = 12

A: Given: Find all the units in Z12

Q: Using only a simple calculator, find the values of k such that det(M) = 0, where 4 k M 1 k As your…

A: M=-4K011K11-8detM=-4-8-K-K-8-K          =32+4K+8K+K2          =K2+4K+8K+32          =K+4K+8

Q: Suppose that 0.3210 approximates 0.3245. How many significant digits does the approximate have? O 3…

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Q: Let n be a positive integer, then n+1≥ for all n.T/F

A: We need to show that n+1≥n for all n where n is a positive integer. Lets proof by contradiction

Q: Find the solution of the sequence of Fibonacci numbers satisfy the relation fn=fn-fn-2 with initial…

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Q: Compute V(X) (in GB2) using the shortcut formula. (Enter your answer to four decimal places.)

A: Introduction: A random variable is a variable with an unknown value or a function that gives values…

Q: 1.N= 2500, e = 0.05 2.N= 486, e = 0.01 3. N=930, e = 0.1 %3D %3D

A: Population is a set of elements or subjects for which the study is conducted and a researchers want…

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 5 in.…

A: Let x be the length of one side of the cardboard,  so our initial piece of cardboard is x by x.…

Q: For the given value of n, find all the units in Zn. n = 6

A: Known fact: The units of the ring ℤn are all the numbers less than n and relatively prime to n. That…

Q: Q2) n(x) = x-1 , k(x) = (x – 1)/2, mx) = (x + 8)¯1 (x + 8)-1 Find a formula for ( m onok).

A: See answer below.

Q: =] Verify n(n + 1)(2n + 1) 6 j=1

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Q: For each integer n > 2, let P(n) bè thế för n-1 Eili +2) = n(n-1)(2n + 5) 6. %3D i=1

A: Given                   P(n):   ∑i=1n-1i(i+2)=nn-12n+56,          n≥2

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in.…

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Q: Find the total number of in H.C.F. of n and 36 is 1.

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Q: Using only a simple calculator, find the values of k such that det(M)=0 where M=[10 k 0 1 1 k 1 1 1]…

A: Determinant: The Determinant is a scalar value that is a function of the entries of a square matrix.…

Q: For n EN, Dn = n! n k=0 (-1)k k! Thus, Dn n!

A: Explanation of the answer is as follows

Q: Find the value of c such that enc=14 n=0 Enter an exact value BD

A: Given :∑n=0∞enc=14

Q: Find the largest number ổ such that if |x – 2| < 6, then |2x – 4| < 6, where e = 0.5. Repeat and…

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Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: Given that f(x) = e*. By taking h=10*, where k =1, 2, find approximate values of f"(2.2) using (a)…

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.