Σ (-1) n=1 nyerges for all n20

Q: 5. Give a general form for T(n) for n > 2

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Q: (-1)" n+1 nEN. E = %3D n

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Q: fΣ (α + bk)- 6n and n+1 k-1 (ak- br) = 1 = then ar - n+2 k-1 k-1 O None 3 5. O 2

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Q: 2 Look at the following picture. 000 000 1st term 2nd term 3rd term Prove that the number of…

A: Given:

Q: M -2 3. 5. Find PN. IN P.

A: From the picture, △PNQ ≅  △LNM. Therefore, NQNM=PQLMAnd,PNLN=PQLM⇒PNLN=NQNM. Given: NQ=5 , QM=2 and…

Q: (4x + 1)2 x2 - 5 Find S' if s = s' =

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Q: (a) an = }(n² + n). (b) an = 2an-1 – an-2 with ao = 0 and aj = 1. (c) an = nan-1 with ao = 1. %3D

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Q: 2 3 n a. If n E N, then + + + •+ 3! 4! (n+1)! (Hint: 3! (reads 3 factorial) = 3 x 2 x 1. n! = nx…

A: Induction theory: Let the given statement is P(n). Step-1: We need to check P(n) is true for n=1.(or…

Q: C. n In n n=2

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Q: 2) S(n)-10-2 at n 5

A: Given ,  f(n) = 10 (2)n     ......... (1) We have to find the value at n = 5 Put ,  n = 5 in…

Q: S =Ene 2 n=1

A: Use integral test to determine Whether the series os converges Or not

Q: (-1)"-1 (In n)" 00 23. E n=2

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Q: 4. E=1(-1)k In k

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Q: Σ 9n n = 1 Identify an-

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Q: W25XT 2540.3 7.5= All 20 students in Mrs. Robinson's 1 st grade class put their name in a hat. Each…

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Q: (-1)"(n + 2) 2n+1(n + 1) 4. Compute the exact value of n=0

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Q: Show that n*-n3.5+300n + 234n²log n³ + nVn10 e 0(n*)

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Q: c) n° n° + 2n is a multiple 3 for all n 2 1.

A: To show: n3+2n is a multiple 3 for all n≥1. Statement used: Principal of Mathematical Induction:…

Q: 5) Find the total Ħ of díagonals for af )n=5 b)n=10

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Q: For every n E N, 1+3+5+ ·.+ (2n – 1) = n² + 3.

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Q: (-1)"(n+ 2) 2n+1(n + 1) 4. Compute the exact value of n=0

A: Given series is  ∑n=0∞-1nn+22n+1n+1

Q: all n N we have We apply this successively for n = bn+1 bn N, N+1, n 9 bN+1 < (m + €)bN bN+2 < (m+…

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Q: n°(r + 4)" 2 .n20/3 infinite, type "infinity" or 'inr".

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Q: (-1)"(n + 2) 2n+1(n + 1) Compute the exact value of n=0

A: The ratio test can be used to assess if a series is converging or diverging. The following are the…

Q: For a population. N = 17, 000 and p = 0.11 Find the z value for hat p =0.26 for n = 60.

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Q: Find the largest value of n such that: Σ E (9k – 5) < 3000 k=1 n =

A: We expand the sum and use the know formulas of "sum of first n integers"

Q: n- (1) Sn n!

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Q: f (n) = 10 · 2" at n= 5

A: We can evaluate the function as below

Q: 8. If n+1, 2n-1 and n+5 are in AP. Find the value of n

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Q: The series k=1 3k (k² + 1)“ + 20

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Q: IF X-N(47, 225). Find the z-score of X=53 O A. -0.4 O B. 1.25 O C. None of these O D. -0.73 O E. 0.4

A: In question, Given that X~N(47, 225). Then we'll find the z - score of X = 53. The solution is…

Q: Show that...

A: We have to show that: n1=nn-1 for n≥1. We know the formula, nr=Crn=n !r ! n-r ! Applying above…

Q: Suppose that E-1 ak = -2 and E=1 bk = 5. Find the values of n k=1 and n 2(ak + bk) k=1

A: To find the values

Q: 3. In experiments, it is shown that on average only 1 in 10 wells drilled produces oil. Let x be the…

A: Given,on average only 1 in 10 wells drilled produces oil.So p=probability of successp=110=0.1

Q: n(n – 1) is O(n²). 2 Show that

A: f(n) is O(g(n)) if there exist positive constants c and k such that f(n)≤c g(n) whenever n&gt;k.…

Q: In n n + 1 а) аn b) an = n n 1+ (-1)" c) An 1 d)an n II

A: Note:  Since we can solve at most three subparts in a question, we have solved the first three…

Q: Q.8 Í xPn+1®n+2dx= Evaluate: n+1*n+2° -1

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Q: 3. Evaluate |(n + 1)! - (n + 2)!|, where n E N.

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Q: ) 1+3+5+ ...+ (2n – 1) = n² for all n > 1.

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Q: The number N of deer in a certain population t years after observation began is given by  N =…

A: Given: The number N of deer in a certain population t years is To find: The deer population after…

Q: -6an-1 for n > 2 with the initial condition a = -9. an an

A: Given an = -6an-1

Q: a series.) 5" In n ω Σ 2" (a) > (b) (c) (d) Σ 4n+3 2n

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Q: Use Gauss’s trick to determine H(n) = 1 + 5 + 9 + 13 + … + (4n – 7) + (4n – 3) + (4n + 1) I'm…

A: Explained below

Q: For a populationN = 22,000 and p = 0.14 . Find the for hat p =0.32 for n = 50

A: The value of p hat is 0.32, the sample size n is 50 and the value of p is 0.14.

Q: n! > 2^n for all n> n0. Make a table to compute the value of n0.

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Q: How would you represent the sum 3+7+11+15+ 19 with the sigma notation?. E(4k – 1) k=0 E(3+ 4k) k=1…

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