k+4 n(3n +7) k(k +1)(k + 2) 2(n+1)(n+2) k=1

Q: >k = 1 + 2 + 3 + · · · + n = ... k= n (п + 1) (b) (а) п! 2 п (п + 1) (2n + 1) (d) (с) nk

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Q: zn 3n+1 7. 4-2n nニ」

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Q: 2 22 k=2 +4 +6+....+2 n= n +n_for all n> 1. 1.- 1

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Q: k と(-1)* k2 +1 k=1

A: LEIBNITZ TEST According to this test, a series of the form ∑k=1∞-1k·ak ; ak>0 will be converging…

Q: 3-n (a) - 3n n=1

A: According to guidelines we solve one question.thanku

Q: Using mathematical Induction Principle 2. If 2 is a factor of k2-k+2 then 2 is a factor of…

A: 2 is a factor of k2-k+2.  That is, k2-k+2=2m,   where m∈ℤ

Q: Coefficient of x³y z² 15. What is the numerical coefficient of the term containing x³ y z² in the…

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Q: K+1 – /K k=1 VK² - +K

A:

Q: 8. k! k k=1

A: given series ∑k=1∞ k!k3

Q: Q1/ Using binomial formula to expand (5+A)5 . Q2/ Find the instruction point of the line 3x - 2y =0…

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

Q: K CK-1) In(k-1) k-3

A: To find if ∑k=3∞kk-12lnk-1 is convergent or divergent: ∑k=3∞kk-12lnk-1 is convergent. To show this…

Q: how to solve 3Fn-Fn-2=F+2 n>3

A: As per Bartleby guidelines, for more than one question is asked, only one is to be answered. Please…

Q: () ( k k+1 П П k+1 \k=1 k+2 k=1

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Q: (2n- 2. Give a combinatorial argument to show that k- ways the number of ways to select a committee…

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Q: Σ(-1)사2(1+ k k-1

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Q: Subtracting (10u³ – 3u² + 4u +9) from (5u² – 7u + 12) the result is O -10u³ + 8u² – 1lu + 3 O 10u³ +…

A: Do the algebraically substraction. Substract the numerical terms of each variables of similar terms…

Q: 5 (K+1) K=1

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Q: (n - 11n +17n + 16) divided by (n– 3) n2 - 8n-6, remainder -6 n- 8n - 7, remainder |

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Q: 16) k(n) = -2|-3n|; Find k(3 + n)

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Q: n 2"-2.n . (n- 1) - Σk(& -1) () | k=2

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Q: a. 2+4 + 6 +8+10 + … + 2n = n + n² ... b. 1+8+27+ .. + n³ = n² (n + 1)2 %3D c. 2+5+8+ ... + (3n – 1)…

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Q: 1 Σ (-3)²+" (n² + 1) -(4x – 12)" n n=0

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Q: Sum 2. Sum 3. 1 (4x³ +16x4-44x² – 24x) and (2x² - 6x³ +2x) ² + ax + b such

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: n-1 n- n-1 n-1 () %3D h - 1 h-p n-1 n-1 P-h = q h-p n-1 ()* (1 -4) n-1 %3D n-1 h - %3D

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Q: 1 4. Σ k-0 (k + 1)(k + 3)'

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Q: 5 -4 -2 3 2 2.) -1 6 -5 1 -31 7 4 -7 1

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Q: C=k-2 express ((c^2)-(k^2))-2 in terms of k

A: C=k-2 express ((c^2)-(k^2))-2 in terms of k

Q: Proof: For n = 0 the result holds. Now suppose that n > 0 and that our assumption holds for n – 1.…

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Q: (a) Complete k (-1)* 2k+n = -½(x) k! (k + n + 1)! k=1

A: Solution a: Given ∑k=1k(-1)kk!(k+n+1)!x22k+n=-J?(x)            (1) Since we know that…

Q: n(n + 1)(2n + 1) 6 k=0

A: In this question, we prove the sum of squares of natural numbers.

Q: n | 0 < k <n n k- 1 k k 1 k = 0 or k = n. %3D

A: An equality is given. We need to establish the given equality. The solution is explained below.

Q: k + 5 / k + 1 + 8 / k^2 -1

A: We have to simplify the given expression k+5k+1+8k2-1. We know that a2-b2=a+ba-b Therefore,…

Q: 2n+2 – 3" Σ - 2. Determine 6n+1 n=0

A: To find: ∑n=0∞2n+2-3n6n+1

Q: 1 Σ (k + 2)(k + 3) k =1

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Q: (a) Complete k (-1)* 4 k! (k +n+ 1)! 2k+n = -½(x) k31

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Q: The series k=1 3k (k² + 1)“ + 20

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Q: П n -k 1+ i=1

A: Solution is attached below

Q: 2(-1)n-1_6" n=1 5n+1

A: To find: ∑n=1∞-1n-16n5n+1

Q: n Σ k + 2n + n2 | n k=1

A: use the sum of first natural number  to evaluate the sum

Q: 9. Sums of squares Show that the sum of the squares of the first n positive integers is n n + (n +…

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Q: ди k = N k > 0

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Q: Find the sum.

A: Given: The sum ∑k=36k-5k-1, To find: The value of the given sum.

Q: Σ 2n+3 + n2 +3n n-1 3.

A: Given series ∑n=1∞1n2+3n+2n+33n

Q: Q1/ Using binomial formula to expand (5+A)5. Q2/ Find the instruction point of the line 3x - 2y =0…

A:

Q: Σ 2n (2n - 1)2(2n + 1)2 n=1

A: The given series is: ∑n=1∞2n2n-122n+12 By the result of Comparison test, if ∑un and ∑vn are two…

Q: 6. A boy notices a group cof birds on the ground and a second group in a tree. He also notices that…

A: Let there are g birds in the group of birds on the ground and t birds in the group of birds on the…

Q: When converting repeating decimals into fractions, is it possible to sometimes get a fraction that…

A: Note: As there are two separate questions posted, we will answer the first question according to…

Q: 2) . (4а — 2)2n+1 n! n=0

A: Given series is ∑n=0∞4x-22n+1n!

Q: Simplify:

A: kk+12k+16+k+12

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.