Let a, be the n th digit after the decimal point in 2n + 6e. Evaluate an(.1)". n=1

Q: Use Mathematical induction to show that H sub(2^n) is less than or equal to 1 + n.

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Q: Show that log, q is irrational for any distinct prime numbers p and q. (Distinct here p# q.) means

A: To Determine :-  logp q is irrational for any distinct prime numbers p and q.

Q: Let Fn denote the nth Fibonacci number. Show that F1+...+Fn = Fn+2-1

A: Using Principle of Mathematical Induction,  Step1: Check for n=1. Step2: Assume the the statement is…

Q: 1 of 2 0.005 0.0025 0.025 0.001 -/1 IND O

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Q: Let f(sub-n) denote the nth Fibonacci number. Show that f(sub-n) is even if and only if n is…

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Q: veight of 7 lb stretches a certain spring integer if necessary.

A: let w be the weight placed at the end, let x be the stretch in the spring Given that the stretch in…

Q: The upper limit of the number of primes less than 23456 is O 2612 O 2331 O 5367 O 7136

A: Given number is 23456. We have to find number of primes less than 23456. formula for the number of…

Q: For each nonnegative integer i, what is the least residue modulo 9 or 10i?

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Q: Express the repeating decimal as the ratio of two integers. 1.11123 = 1.11123123123...

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Q: Find all values of In(-e")

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: a) Find the population after 7 years. (Round to the nearest integer as nee

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Q: Find the geometric mean between 5 and 45. Express answer in exact form as a simplified radical O…

A: Given that: Two numbers are 5 and 45.

Q: Let an be the nth term o structed by including the

A: Given, an be the nth term of the sequence                    1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5,…

Q: Fn denote the nth Fibonacci number.

A: Given,              A=1110 To prove that,              An=Fn+1FnFnFn-1

Q: Suppose 1.34 % of the items produced by a particular assembly line are defective. How many items…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose 3.141516 is estimated using 3.141529. The absolute error is (Answer must be in 6 decimal…

A: We need to calculate the absolute error when 3.141516 is estimated using 3.141529

Q: 5n. Determine for which n n-2 For nz 2, let on =

A: Here we have to determine the n for which |an|<1 for all n≥2 where an=5nn2-2

Q: Denote by fn the nth Fibonacci number. Show that when n is a positive integer, fofi + fif2 +.+…

A: Write recursive definition: f0=0f1=1fn+2=fn+fn+1

Q: Let an be the n th digit after the decimal point in 6T + 4e. Evaluate Σα. (1)" an n=1

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Q: Sx" Inxdx

A: The given integral is  I=∫xn ln x dx after solving this we have to use the result to find the below…

Q: Let An be the n th digit after the decimal point in 6n + 4e. Evaluate am(.1)". n=1

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Q: If nCr = 65536 determine the value of n.

A: Four basic operations defined on numbers are addition, subtraction, multiplication, and division. If…

Q: 1 ιπ 1s +472, e where n is an integer.

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Q: 27 en+1 – 1 < 0.05 ? 2 (n + 1) · (n + 1)!

A: Given: The expression is, 272en+1-1n+1n+1!. Calculation: Obtain the value n such that…

Q: Prove that the nth Fibonacci number fn≤αn−1, where α is the golden ratio.

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Q: Use the formula to compute In(1.11) correct to five decimal places. In(1 – x) = - x" n = 1 In(1.11)…

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Q: For a population, N = 20,000, μ = 125, and σ = 25. Find to 2 decimal places the z value for for n =…

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Q: use Hew Find the natureof the fallowingsekies 3-s ncn+i) nel hth=termtest- { Ln to to en 4- n² +3 en…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: Let N=20. Show using the Sieve of Eratosthenes how to find all prime numbers between 10N and 10N+100…

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Q: Consider all numbers between 20000 and 70000. Efficiently determine: A) How many of these numbers…

A: Part A - Let’s represent the number as ABCDE. You have to considere the special cases first, since…

Q: Which is larger  2^100 or F100 with F representing a Fibonacci number? Prove which is larger.

A: Increment in each term in Fibonacci series = FnFn-1  Increment in each term in 2n series = 2

Q: Show the p in th

A: Vertices of the triangle is Given integral is

Q: Evaluate In(0.473). Give your answer to four decimal places.

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Q: Let an be then th digit after the decimal point in 3T + 7e. Evaluate Ean(-1)". n=1

A: This is a problem related to sequence and series part. based on the general formula available for…

Q: Let an be the n th digit after the decimal point in 67 + 5e. Evaluate Σα. (1)". n=1

A: Since, it is given that an is the n th digit after the decimal point in 6π+5e. Our Aim is to…

Q: Show that the n-th tetrahedral number O_n is given by S_n= n(2n^2+1)/3

A: A tetrahedral number corresponds to a 3-Dfigure in the shape ofa tetrahedron made of spherical…

Q: Find th: units digitof 3" ++ 11* ", whe re e and n: arc: nan-npitve intrgers

A: To solve this question we need to find out unit digit of each term and then add these unit digits to…

Q: Draw a number line on which adjacent tick marks are 0.1 unit apart and on which 0.003 can be plotted…

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Q: Vhat's the index and radicand of: V6a ?

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Q: n that includes all terms up to

A: The initial value problem is , w''+7xw'-w=0. It is given that w0=6, w'0=0. w''+7xw'-w=0. To find the…

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

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Q: on 10 of 16 25628 49977 376? Find the missing number? O A) 40 O B) 38 OC) 39 O D) 35

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

A: The given repeating decimal is 0.3  let xy=0.3 where xy is the required quotient of integers…

Q: Find mZD. 6. D Write your answer as an integer or as a decima mZD = %3D

A: We have a right-angled triangle right angled at F we have to find angle D

Q: An object thrown upward from the ground falls to the ground after k seconds. Which of the following…

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Q: A study of n = 2252 adults age 18 or older found that 72% of the cell phone users send and receive…

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Q: Decimals can be approximated by using only the leading nonzero digit or by rounding to the leading…

A: Answer : Approximate 0.0081 by using the leading nonzero digit = 8.1 × 10-3

Q: find the z score in which 93.70% of the z scores in a population are below that value

A: In this context, we need to find the value of c. P(Z &lt; c) = 93.7% = 0.937  F(c) = 0.937 = F(1.53)…

Q: To index Qn [6, 20] using N as the index set.

A: We need to find ℚ∩6, 20 and we have the index set is ℕ Now, ℚ∩6, 20=6, 20

Q: Denote by fn the nth Fibonacci number. Show that when n is a positive integer, fofi + fif2 + +…

A: Given: fnis nth Fibonacci number. To show: f0f1 + f1f2+···+f2n-1f2n=f2n2

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.