2+1/n 1+1/n 2n + 1 2 2 for n → o. 1 In n+1

Q: 1 + 1.2 1 1 n for all integers n>1 n+1 3. Prove that %3| 2.3 n(n+ 1)

A: To prove the given statement.

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: B2. Using induction, Prove that 2+ 6+ 10 + ..-+ (4n – 2) = 2n² for all n e N. B3. Simplify the…

A: Mathematical induction is one of the basic proof techniques. When a statement is valid for all…

Q: Find L[14cos28t] 7s s2–256 7. 2s 7s + s2+256 s2+8 7s s2+64 1

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Q: 7+8+9+ 10 +...+ 26 O 25 (k + 1) 9-36 O26 E (k +1) k=7 6T (k+1) k=1 O 27 E (k+1) k=D8

A: Given :-  7+8+9+10......+26

Q: Given the following power series, find the radius of convergence. HINT: Determine if you want to use…

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Q: 2n+2 52n+1 3n+2, 22n+1 is divisible by 19 co dady M N [ day f04+ 204d (21)

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Q: n If E (ak + bk) 2n and n+1 k=1 E(ak – br) +, then ak = n n+2 k=1 k=1 3 2 5 2 O None 2

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Q: The sum of the first n positive odd integers = Check all the correct answer/s. Σ I T Σ(2x + 1) 2=1…

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Q: Σ ∞ n=1 1+4¹+1 6⁰ is equal to

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Q: a+1 n+2 n+5

A: An  Infinite is defined as the sum of the values in an infinite sequence of numbers. Assume the…

Q: -1 The sequencе аn 2n + 3 (a)decresing (b) increasing (c)not monotonic

A: A sequence an is said to be an increasing sequence, if an<an+1, ∀n and is said to be decreasing…

Q: k-1, O A. (n+1)! (k-1)!(n-k)! (n+1) В. (k-1)(n-k+2) OB. С. (n+1)! (k-1):(n-k+2)! D. (n+1)!…

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Q: TL ( - k) = | k-1 a. 6n + (n + 1)(2n + 1) - b. n(n + 1)(2n + 1) c(n²-1) C. O d. n3 e. 00 f. 플 (n +…

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Q: de x² + 3x On|리 + In |z + 3| + C - +C 3z2 1 :In |피- - 승미z + 3| + C 1. :In |z| + 등In|z + 3| + C O In…

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Q: Prove n (2k – 1) = n² - k=1 for every n EN.

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Q: 3 Which of the following expressions are equivalent to 6n2 +12n 18 (n+2) C 6n (n+2) 18n + 38 A 6n…

A: The addition(subtraction) between two like fractions can be done by adding(subtracting) the…

Q: 5. Show that n²(7n – 2) is O(n³).

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Q: n Prove by induction that Σ (− 1) ¹;² = (-1)”n(n+1) 2 i=1 n Prove that Σ i=1 1 i(i+1) = n n+1

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Q: 1 1 1 1 Σ Evaluate Hint: + n(n + 1)(n + 2) n(n + 1)(n + 2) 2n n + 1 2(n + 2) n = 1

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Q: Find the area of each circle, given the radius r or the diameter d. Leave your answer in tems of t.

A: See the detailed solution below.

Q: Q2. Induction. For each integer n > 1, define the sum S(n) as follows: 1 1 1 1 1 S(n) = (2i — 1)(2і…

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Q: 4 Σ n2 +4n +3 - 9-n+24n+1

A: Separate the sum.

Q: 1. The factorial notation n! is defined for a positive number n as n! %3D п (п — 1)(п - 2)...…

A: Questions: 1. The factorial notation n! is defined for a positive number n as, n!=nn-1n-2...3210. 2.…

Q: if x[n] = u[n+1] −4u[n]+u[n − 1] +2u[n-2], which of the following answers is correct? A. x[n] = 6[n+…

A: We know, by properties of u[n] and δ[n],          δ[n] = u[n] – u[n - 1] We use this property to…

Q: 1(1!) + 2(2!) + ..+ n(n!) = (n + 1)! – 1. %3D 3.

A: (3) The given expression in the LHS can be written in the form of series as, ∑n=1nnn! Now solve the…

Q: If (ar + bx) 8n and n+1 k=1 n Σ (α- br) 1 1. then ar n | n+2 k=1 k=1 O 2 None 9. 2 5 2 3 2

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Q: 5. Find and prove a formula for P(n,n-2) for n2 3.

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Q: (":')-(:)·(,".) n +1 n n - Prove that for all integers n > i > 1. i 1

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Q: 1. 1.1! +2.2! +3.3! + ... + n.n! = (n + 1)! - 1 for all n ≥ 1

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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: Evaluate the sum 1 Σ² n! n=0 1 + (-1)^²+¹ + (-2)' (−1)n+1 n 2n+1

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Q: For all n E N prove that 1 3 2n – 1 1 - 2 4 2n V2n + 1

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Q: 4n² +14n+1 = Let P(n):9+13+...+(4n+5) 2 Show P(k)→ P(k+1). Does this mean P(n) is true Vintegers n ≥…

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Q: n (A)-0) k Simplify the equation shown here. with n≥k and n, ke Z+ (In the answer choices, nCk…

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Q: 1. The factorial notation n! is defined for a positive number n as n! = n(n – 1)(n – 2)...…

A: As per bartleby guidelines only 3 subparts are answered, please upload the rest separately. The…