4) Find the Σ Σ _n=1 SUM of the following series (a₁ +n) (a₁ +n+1)(a+n+2) (af-n, nEN)

Q: Write each series in summation notation. 1 + 10 1 1 1 1. -2 + 4 - 8 + 16 – 32 2. 100 1,000 10,000 1…

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Q: 4 5 + 2+ 8 25 Sum:

A: Geometric Series Question

Q: Find the first four terms of the finite sequence an= 3n A.3,6,9,12 B. 3, 7, 10, 13 C. 1, 3, 6, 9 D.…

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Q: 75k+1 (c) Σ cos(1)2k k=1 Geometric Series Test p-series Test Limit Comparison Test Divergence Test…

A: ∑k=1∞ π5k+1cos(1)2k  =  ∑k=1∞ 1cos(1)2π5+1/kk        -Hence, p-series test is possible=…

Q: Find the sum of the series. 2* + 1.3 2.32 3.33 4.3* 2 22 23

A: Sum of the series, using maclaurain Series expansion

Q: 6.25 1+z6 as a power series. 2. Using your answer in 1, write In |1 + x| as a power series. 1. Write

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Q: Determine the sum of the following series (hint: the answer will have the variable k): 4k + 11k +…

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Q: Find the infinite sum generated by the following series: 4+1+ 4 16 ... 16 3. O O

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Q: Find the sum of the first 5 terms of the geometric series. 8 – 16 + 32 – ... 87 86 88 89

A: We have to solve

Q: Find the sum of each geometric series. 1. 36+6+1+...; S10 2. a1=1, r=4; S6

A: Find the sum of each geometric series.  1. 36+6+1+...; S10 2. a1=1, r=4; S6

Q: Determine the sum of this convergent series.

A: This question can be solved using the concept of infinite geometric progression.

Q: Determine whether the series Conreges. If it cantages, find its som. If it diverges. explain why. W…

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Q: Find the arithmetic series of the arithmetic sequence (1, 2, 3, ., 250}. a 31,375 b 31,250 31,125 d.…

A: Given arithmetic sequence is  ={1,2,3,....,250} Formula of sum of arithmetic series is  =(n/2)(a+l),…

Q: Find the sum of the infinite geometric series.

A: For | r | <1 S∞=a11-r

Q: 3. Consider the sequence a, =an-1, with a, = 6 and evaluate the following summation. ak k=1

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Q: Find the sum of each of the following series.

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Q: Consider the following sequence. 6, 18, 54, 162,    Find the sum to 10 terms. s10 = ? If the…

A: 6,18,54,162,.... Formula Sum of n terms Sn=a(1-rn)1-rSum of infinityS=a1-r

Q: find the third. fourth and fiAth partial sums of the series, 8(-5)" n-1

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Q: Determine the sum of the first 14 terms of the following series: 2 – 6+ 18 – 54+.. - -

A: First of all find all 14 terms using logic then add them

Q: - Find the sum of the given series. 1 1. 1- 3! 1 1 5! + ... 7!

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