For Exercises 41-46, find the sum of the geometric series, if possible. 7 \i-1 41. 5(3)"- 42. E 12 n=1 i=1 k-1 43. 44. (4)'-1 n-1 4 46. 36 – 12 + 4 3 45. - - ... n=3 + * IM:

Q: (b) (i) The sum of the following infinite geometric series exists. Briefly explain why. Find the…

A: we have to find the common ratio and the sum of the given geometric series

Q: Find the indicated term of the sequence. an = (-1)^-'[n(n – 2)] %3D a19

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Q: write down the first five terms of each sequence

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Determine how many terms are required for the sum of the series 10k2 – 4k + 2, k = 1,2,3, ... to…

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Q: 1. The general formula for a sequence is t = 2t₁-1 — n, where t₁ = 5. Find the fourth term.

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Q: State the first 4 terms of each sequence, then explain why each series is convergent, divergent, or…

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Q: n-1 (– 1)"(÷)" 49 Find the sum of the series: 2n + 1 n=0

A: We have to find the sum of given series.

Q: 49.: * How many terms of the series do we need to add in order to find the sum to the indicated…

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Q: 00 For an as follows, write the sum as a geometric series of the form > ar". State whether the…

A: Solution: The objective is to find the sum of the series

Q: 43.- Study the following series of numbers, which number should go where the question mark is?

A: check out the sequence and find the missing number.

Q: 1 2 30x(x − 1) ¹ dx is

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Q: n-1 (- 1)"(÷)" Find the sum of the series: 2n + 1 n=0 2788.625

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Q: 30. Ifx', 4x + 3, 25 are in geometric sequence, find the values of x. а. -1/3 b. 1/3 or -3 с. -3 d.…

A: x2 , (4x + 3) , 25 are in geometric sequence,  Hence, ratio of successive terms is equal to the…

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: Find a formula for the nth term of the sequence (choose one of 2) The sequence 2,6,10,14,18, ..

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: The third term in the arithmetic series is 14. The sum of the second and sixth terms is 34.The sum…

A: Given third term of the sequence is 14 and sum of second and sixth term is 34 . We have to find the…

Q: What is the sum of the series represented by . (2n + 5)? n=3 Enter your answer in the box.

A: The given series is: ∑n=37(2n+5)

Q: 1. 3n+1 3. n2 + 5n + 6 3-2п 2. 4. (n – 1)? | n+1

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Q: Find the sum of the first 6 terms of the geometric series if a1= 1 and r = 2. 36 63 O -63

A: Given problem is :