n(n+1) for all n EN, • Given that 1+ 2 +3+..+n = the sum 70 + 71+72 + .+ 100 = 2

Q: The infinite series Σ n=0 2n n³ - 5 - is

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Q: Find the sum M "n=√n²+1 n=1 -√n(n+1) Ž noi 1 4n²-1 acasmu n=1 ((1+1)(n+21)

A: Introduction: Similar to a sequence, an infinite series can be convergent or divergent. When a…

Q: Find the partial sum. 100 60 En-In n = 61 n = 1

A: Given,

Q: How is the series 4+9 + 14 + ·..+ 244 represented in summation notation? 40 Ο Σ6η+4 n=0 40 Ο Σn+4)…

A: Given: S=4+9+14+………+244 The given series is an arithmetic series with a common difference(d) 5. The…

Q: Find the sum of the series or show that the sum does not exist. a. I (In 2)"-

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Q: 5. Show by mathematical induction that the geometric sum can also be written by Zar' = a+ ar + ar…

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Q: The sequence {bn}∞n=1 is defined as b1 = 5 , b2= 13, bn = 5 bn −1 − 6 bn −2 for n ≥ 3. Prove bn…

A: 8 Given that the sequence bnn=1∞ is defined as b1=5, b2=13 and bn=5bn−1−6bn−2. We have to prove that…

Q: Suppose that > an = Σ 5 and > bn - 3 and a1 = 7 and b1 = 8, find the sum of the series: n=1 n=1 E…

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Q: Find the sum 24 n=1 - n(n+1) हैं ये aca n²+1 ni 4n²-1 ΣLn/n (2n+1) (+1)(n+21. n=1

A: Introduction: Like a sequence, an infinite series can also be convergent or divergent. When the…

Q: show that for all N in N * Σ (2/(n(n+2)=3/2 - 2N+3/(N+1)(N+2)

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Q: Find the sum of the series. Σ 5(-1)"72n + 1 32n + 1(2n + 1)! n = 0

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Q: 4 Σ Find the sum of the series (2n - 1)(2n + 1) n= 1

A: The explanation of the solution as follows:

Q: Does there exist an N such that SN > 25 for the series 2-"? Explain. 00 n=1

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Q: What is the summation from n = 1 to infinity, of  (3n+1) / (5n + 4) ?

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Q: 5 Compute the sum: 3n

A: Take 3 out of the summation and the use the formula for sum of n natural numbers.

Q: The series expression for 1 1.4. 1.4.7 1:4.7.10 2 8 32 128 (n+ 1)! Σ n=2 (n- 2)! (–1)^+1(1 -4·7- (3n…

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

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Q: 2. Suppose n > 2 is an integer. Identify a sequence of n – 1 consecutive positive integers none of…

A: het n72 . be aninfegerThenofsequencecomposite numbers(n-1)consecutiveoren!+2, n !+3,in! +(n-1)These…

Q: The series E-, 2k (-1)*+1 is 'k% D = 1

A: Using comparison test to find type of series. If series of absolute term is divergent then series is…

Q: Find an explicit formula to calculate the sum (assuming n is a multiple of 2)  P = 1 · 1 + 2 · 2 +…

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Q: Find the sum of the series. Σ 62n + 1, 5(-1)^72n + 1 1(2n + 1)! n = 0 8

A: According to the given information, it is required to determine the sum of series.

Q: The Fibonacci sequence is defined as an=1,1,2,3,5,8,13,....  Where a1=a2=1 & an=an-1+an-2 Prove by…

A: Given: The Fibonacci sequence is defined as an=1,1,2,3,5,8,13,.....where, a1=a2=1 & an=an-1+an-2…

Q: Σ Suppose that an 8 and > bn - 2 and a1 9 and b1 = 1, find the sum of the series: %3D n=1 n=1 E(-…

A: Given ∑n=1∞an=8∑n=1∞bn=−2Also, a1=9,b1=1

Q: Evaluate the sum from k=0 to 4 of ((-1)^k(k+3)^2+3)

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Q: Suppose An = 2n^2 + 6n + 6. Find the closed formula for the sequence of differences by computing An…

A: As per our question, we need to find the closed form of an-an-1×an-an-1 First find an-1 and then…

Q: How is the series 2 + 6 + 10 + ... + 86 represented in summation notation? 21 Σ(4k + 2) k=0 21 Σ(4k…

A: The objective of the question is representation in summation notation.

Q: 17. Compute the sum Σ -2k k=1

A: To find - Compute the sum ∑k = 1∞-2k

Q: Prove { (8n-7)/n} n=1 to infinity is an increasing sequence.

A: If we take the sequence as {Un}, and if we can able to show that for all n=1,2,3, ...  Un+1>Un…

Q: 00 Suppose that > an = 2 and bn -1 and aj = 4 and bi - 6 , find the sum of the n=1 n=1 series: 00 А.…

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Q: Use Gauss' trick to determine the sum 1+3 + 5 +... + (2n – 3) + (2n – 1) + (2n + 1

A: Gauss's trick is very significant in determining the sum of a series. This method includes the…

Q: Suppose that an = 3 and 9 and a, = 6 and b 4, find the sum of the series: n=1 n=1 А. 7a, + 3b,) n=1…

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Q: 2. Define sequences (an) and (bn) by letting an-1+ bn-1 an = bn = Van-1bn-1- Deduce from the…

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Q: Find the sums of the series

A: We have to find the sum of series: ∑n=3∞12n-32n-1 Putting n=3 to ∞,…

Q: The sum of the series > 2"+23n is n=0

A: Given : ∑n=0∞2n+23-n

Q: Σ n2+3n+2 n=1

A: The given series is: ∑n∞1n2+3n+2  We have to find sum of this series.

Q: Suppose that 2 and b, = 4 and a1 - 6 and bi - 5, find the sum of the series: n=1 n=1 A. E(- 3a, +…

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Q: Find the sum of the series: Σ n=0 - − 1)" (12/12) " + ³ 25 2n + 1 (

A: Sol:- Given series can be re-written as…

Q: Find the sum of the infinite series. 1 1 1 6-18 18- 30 30-42 +... 42-54 (Use symbolic notation and…

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Q: Find the sum of the series. s 7(-1)"72n + 2n + 1(2n + 1)! 00 Σ n = 0

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Q: . Therefore the series >

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Q: Prove that the sum of the first n natural numbers is given by this formula: n(n + 1) 1+2 +3 +. ..…

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other questions as…

Q: Find the sum of the series. 7(-1)"72n + 1 32n + 1(2n + 1)! n = 0

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Q: 14. Find the Sum of: 1 in(n+3) In (n+2) ニ

A: To find the sum of the given term

Q: Find the sum n-√n²+1 Mn n=1 --√n(n+1) 4n²-1 acamu Σ "Ln/n (2n+1) ((₁+1)(n+21.

A: Introduction: An infinite series can be convergent or divergent, just like a sequence. The sum of…

Q: 1.)Prove that every n ≥ 14 ∈ n can be written as the sum of sequences of 3's and 8's

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Q: Find the sum of the series: 3n+2 - 2n-1 4n n=1

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Q: Suppose that the nth partial sum of a series (∑∞n=1  an) is sn = (n+1) /( n+2). Find an.

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Q: show that the sum of this: pi/(3sqrt(3))=(∑∞ n=0 ((-1)n (1/2)3n+1))/(3n+1) + ∑∞ n=0  ((-1)n…

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Q: Let n be a positive integer. Suppose we choose a sequence i1, 12,..., in of integers between 1 and n…

A: Given, Let n be a positive integer. Suppose we choose a sequence i1,i2...in of integers between 1…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.