[3n+ 2 (-1)A In 3n + 6 n=1

Q: („*.) (* ) =(). 2n 2n 2n + 2 (c) Verify that + n +1 n + 1

A: According to the guidelines we are supposed to do one problem

Q: 1. Find the indicted term: an = (3n+ 2)²; a6

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Q: 40. Ifn is any positive integer, then (n- 1)(n-2Xn - 3) ... (3(2X1) = A e B. (n-1y C. n! D. (n-1

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Q: Prove, by induction, that n + 3n2 + 2n is divisible by 6, for n 2 0.

A: In this problem I have use mathematical induction method two times please read step by step.

Q: n-1 For all n > 2, 4+ 3n4" – 4n+1 - j=1 9.

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

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Q: Show that2/31 + 2/32 + g+ 2/3n = 1 - 1/3nfor all positive integers n.

A: The given series is the geometric series, hence the formula to find the sum of the series helps to…

Q: Show for all integers n> 1 that 7 I (3ªn+l – 5²n-1 ).

A: a) Prove 734n+1-52n-1 for all integers n≥1 by mathematical induction as follows. Basis step: For…

Q: 2n+1+(-1)" Prove that for all integers n 2 0, 3.2"

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Q: Find all integers n > 1 such that 1n − 1)" is +2+...+(n divisible by n.

A: To find all the integers n>1 such that 1n+2n+...+n-1n is divisible by n

Q: 1 1 1 17. II П for every integer %3D 2i +1 2i+2 (2n +2)!’ n20.

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Q: Prove that πd/n n = nτ(n)/2.

A: your question has a silly mistake, it should be πd|n d = nτ(n)/2. supposeτ(n)=r , where r be the…

Q: -92 -20 -32 - -424 -90 -154 512 110 182 What is A5? . A = 1 -3 -2 1 5 :) ( 7 0 4 0 0 8 10 0 (39 8…

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Q: . Prove that 2 +4+6+•…+ 2n = n(n + 1) for all n > 1.

A: According to the given information it is required to prove

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

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Q: a) Verify this equation using mathematical induction that for all n2 1, n(3n – 1) 1 +4+7+ ·.. + (3n…

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Q: Prove that n3 + 2n is divisible by 3 for all n E N.

A: We prove that n3+2n is divisible by 3 for all natural numbers n.

Q: Can you assist  me in  verifing    that    for    all    n ≥ 1,    the    sum    of    the    first…

A: Here, we have to verify that ∀n≥1, the sum of the squares of the first 2n positive integers is given…

Q: Is 12n + 18 equivalent to (2n + 6) (n + 3) ? True O False

A: Answer: True.

Q: r(r+1) n+1 8. Prove by mathematical induction that 5"-4n - 1 is divisible by 16, for all positive…

A: As per our guidelines we are supposed to solve only one answer . Please repost another question as…

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

A: The geometric series formula is ∑n=0∞rn=11-r, where r<1. Simplify the numerator of the given…

Q: 1 + 2n < n° for all integers n² 2

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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: Use the factor theorem to verify the statement

A: Consider the statement  x−y is a factor of xn−yn for every positive integer n.

Q: If a_1=9a1​=9 and a_n=4a_{n-1}an​=4an−1​ then find the value of a_5a5

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Q: Prove the statement by induction .+ (4n – 2) = 2n² 2. 1+ 4 + 7 + . + (3n-2) = n ( 3n - 1) 1. 2 + 6 +…

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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: Prove that 1 + 4 + 7 + ... + (3n-2) = n(3n-1) / 2

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Q: 3. Use the binomial theorem to prove that 2n 2n |22n–2k = (2.5)2". k k=0

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Q: (Vn)(n2 +n+ 17 is prime)

A: Since, you have posted multiple questions , I am doing the very question (ques 7)  according to our…

Q: Prove that2.7n + 3.5n – 5 is divisible by 24, for all n ∈ N.

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Q: Question 7 Is 2 (n? + 6n + 9) equivalent to (2n + 6)(n + 3)? True False

A: Given: 2 (n2+6n+9)≡(2n+6)(n+3)?To find whether it is true or false?

Q: Σ Ea = n². %3D k=1

A: It is given that,  ∑k=1nak=n2

Q: Show that, for n > 1 2n 1.3.5... (2n – 1),2n 2.4.6...2n n

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Q: Prove that n² +n is divisible by 2, where n E N.

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Q: prove by mathematical induction + E+ 7.16 +.. 1 1 (Зп-2)(3п+1) 3n+1

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

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Q: Let a1 = a2 = 1 and suppose an = an-1 + an-2 for n ≥ 3. Prove that a1a2 + a2a3 + · · · + a2n-1a2n =…

A: We have given that , a1 = a2 = 1 Also , an = an-1 + an-2 We need to prove that ,  a1a2 + a2a3 +…

Q: If (ar + bx) = 4n and n+1 k-1 (ak - bx) = , then > ak = n+2 k-1 k-1

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Q: Verify that for all n ≥ 1, the sum of the squares of the first 2n positive integers is given by the…

A: Verify that for all n ≥ 1, the sum of the squares of the first 2n positive integers is given bythe…

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

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Q: 17. The coefficient of x²y² in the expansion of (2x + 3y)4 is O 186 O 216 O 124 none of these

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Q: het A=" and let fce)= 20x²-4X+5. Find 3 4 -3 り 3 4 ) fCA)

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Q: Find the possible values of n. (n2 )" – 2n" + 1 = 0 (n +0,1)

A: We have  n2n-2nn+1=0 and n≠0,1 We can write n2n as n2n=n2n=nn2 So, nn2-2nn+1=0 Let nn=x x2-2x+1=0

Q: A. Prove that n3 + 2n is divisible by 3 for all integers n.

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Q: 3n – 5n is n→ o n° - 2n² +1 lim 3

A: It is given that, limn→∞3n3-5nn3-2n2+1.We have to evaluate it.

Q: 24. 2n(ar31) In(3 +1)-3n(x)

A: To simplify using the properties of the logarithm the expression given below:

Q: a) By using mathematical induction, prove that the given equation is true for all positive integers.…

A: I will Solve (a) For you. Given, 2+6+10+.......+(4n-2)=2n2 We have to prove this equation is true…

Q: Show that: (n-2)a2 ~X2 (n-2) o2

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Use the factor theorem to verify the statement

A: Given statement is, x+y is a factor of xn-yn for every positive even integer n.   So, Let fx=xn-yn,…