E If the mth term of an A.P. is 1 and the nth term is 1 1 show that the sum of mn terms is ( mn +1).

Q: Based on Theorem 4.4.3 P.169, when n > 2, which of the following is biggest? 1. n! 2. n^n 3. (n!)^2…

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Q: Suppose a ball is thrown upward to a height of ho meters. After each bounce, the ball rebounds to a…

A: We have given h0 = 15, r = 0.25

Q: Suppose a ball is thrown upward to a height of ho meters. After each bounce, the ball rebounds to a…

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Q: The sum from k=1 to infinity of: [(5sin2k)/k!]

A: Given,

Q: Suppose it was known that the cells ofa given bacterial culture divide every 3.5hours, if there are…

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Q: IC years older than Carolyn. John Will John is now In Byears Carolyn will be then. How old is each…

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Q: In each case, find the first 5 terms of the sum and compute S. 31-1 r: The first 5 terms are: The…

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Q: How many terms are required to ensure that the sum is accurate to within 0.0002? 00 n=1

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Q: The ration of the sums of m and m terms of an AP is m2:n2 .show that the ratio of mth and nth  is…

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Q: In each case, find the first 5 terms of the sum and compute S 31-1 00000 The sum is The first 5…

A: Given data is : ∑i=1n3i-1 Let an=3i-1  where i=1,2, 3,4 ......n Substitute i=1 so first term…

Q: In each case, find the first 5 terms of the sum and compute S, 3. The sum 1S 2 The first 5 terms are…

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Q: (b) Generalize: if the numbers 1 to n are placed around a circle in some order, what is the best…

A: (b) If the numbers 1 to n are placed around the circle in some order, the best possible lower bound…

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

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Q: Express the sum in terms of n.

A: Given- ∑k=1n3k2-2k+1 To find- The sum of n terms.

Q: 8.. If both the terms of a ratio are added with the same non-zero number, the ratio remains…

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

Q: Find the sum of the series 12+17+22+..+777

A: We have to find the sum of the series 12+17+22+....+777. First term=a=12 In the arithmetic…

Q: * :The nth term formula for { 1,0,1,0,... } is 1-(-1)" 2. an = A₂ = An خيار 2 1 + (−1)" 2.

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Q: Suppose Suppose a, = 3n? – 3n – 3. Find a closed formula for the sequence of differences by…

A: Given, an = 3n2 -3n +3  We have to find an-an-1

Q: Evaluate the following sum. E(-1+2i)² i=1

A: Given: ∑i=1n(-1+2i)2

Q: f in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n then prove that…

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Q: Sn denotes the sum of the first n terms of an AP prove that S30 = 3 (S20-S10

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Q: Given the nth partial sum, find a1, an; and £am. n+2 21. Sn = n+3 an E an ||

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Q: The limit of the sequence Zn = Arg(-i + ) is equal to Select one: C. 2 -3T d. 2

A: See the solution in the given fig.

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

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Q: In each case, find the first 5 terms of the Sum and comgute S

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Q: D. Finc the sum to infinity of the geometric sequ ence, 1. E4, 16, 4, 1, ...

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Q: If the mth term of an A.P is 1/n and the nth term is 1/m, show that the sum of mn terms is 1/2(mn+1)

A: In this question we have to prove sum of mn terms is 12mn+1 We know, A.P, for mth termam=a+m-1dand…

Q: 14 For: 等,曾 3. 6. 27 3 5 7 5n 6. ... Find the explicit nth term.

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

Q: 3n+2 4n–2° n=1

A:

Q: 5(п+1) d. an 2n-1 е. ап 5n + 12 II

A: Given: an=5(n+1)2n-1 & an=5n+12 To determine: The first 10 terms of the given sequences.

Q: Find the indicated sum. il Σ (i – 1)I Σ (1- 1)1

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Q: How many terms are needed to make sure that the sum is accurate to within 0.00005?

A: Given: ∑n=1∞ 1(2n+1)2 To find: How many terms are needed to make sure that sum is accurate to within…

Q: The value of the sum E (- ) is given Zk=4 by: Select one: O a. 3 O b. O c. None of these O d. 1

A: Given :                 ∑k=4∞ 1k-3-1k-1 To find :                      The value of sum of given…

Q: A farmer has a crop of 2,000 orange trees at the beginning of this year. Each year, the farmer plans…

A: Given,         A farmer has a crop of 2000 orange trees at the beginning of this year. Each year,…

Q: Suppose that 0.3210 approximates 0.3245. How many significant digits does the approximate have? O 3…

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Q: How many terms are required to ensure that the sum is accurate to within 0.0002? e-n n=1

A: We have to find the number of terms required for the sum to be accurate within 0.0002 .

Q: Determine how many terms of (-1)*+lgk must be summed to be sure that the remainder term k! k=1 is…

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Q: Find the sum S given by S=1² +2²x+3x²+4² x³ +0 for x < 1

A: A good problem. We shall look at the famous geometric series \sum x^n and obtain S by repeated…

Q: With the aid of a power reducing formula, 22sin²a=? |3| Select the correct answer below: O 11– 22cos…

A: We can make it easier for you

Q: Find the total number of in H.C.F. of n and 36 is 1.

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Q: Given the following sequence: 33, 30, 27, 24, ... [2] Write a formula to generate the nh term and be…

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Q: There is a simple formula for the sum of the first n cubes. n' (n + 1)2 n i=1 Using this formula,…

A: Sum of cubes

Q: If 17 %% of a substance de compos es in so ycars, a) what porcent age re main clfter 100 years? b)…

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

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Q: Express each of the numbers as the ratio of twointegers. 3.142857 = 3.142857 142857....

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Q: If t = 3.5n +4.5, find t,, t10 and t Is 85 a term of this sequence? -t 14 n +1 in Answer: %3D %3D In…

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Q: 1. Debermme the number of tems required to appoxnade the Sum of the gren mfinite seves with an ewar…

A: The given series is ∑n=1∞-1n+1n4. The above alternating series have general term an=-1n+1n4. Hence,…

Q: If the mth term of an AP is 1/n and the nth term is 1/m .show that the sum of mn terms is 1/2 (mn+1)

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Q: 16. For what value of n is the following sequence A". If c = 2, find Co. %3D Cn = 2,4,10,23,46,82,…

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Q: the formula of the general term an of th 13,10,7,4 ,..

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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.