Show that 1 1 (r+2)(r+4) 2 r+2 r+ Hence, find the sum of the first n terms of the series 1 +. 4-6 1 3-5 5-7

Q: The simple formula for a, if the first 5 terms of the sequence {an} are 1, 21, 121, 621, 3121 is:…

A: We are asked to find which is correct for the sequence.

Q: Find the sums of the series

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Q: Suppose that 7 and ) b = 2 and a1 = 9 and b 4, find the sum of the n=1 n=1 series: A. >(-8an + -…

A: SOLUTION-

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: Suppose that an = bn = - 1 and a1 5 and b1 = - 6 , find the sum of the 2 and n=1 n=1 series: 00 А. >…

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Q: Find the sum of the series 3n-1 7n n=1

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Q: Find the sum of the series. 8. Σ 3(-1)"72n + 1 22n + 1(2n + 1)! TC

A: Formula: The power series about of a function about is, Given:

Q: A- Find the sum of the following series: 2n=0 2 ()" 2- Σ(- 1)" - (-1)"

A: A. 1. Given: ∑n=0∞215n The above equation can be written as: ∑n=0∞2·5-n Pull the constant out of the…

Q: Find the recursive formula for the series given by 3/4 a1 = 1.5, an+1 = an 3/4"/2 a. a1 = /3/4, an-1…

A:

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

A: The sum is evaluated below.

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

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Q: > 3n+14-n n=1

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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: uppose that an 9 and - 6 and a1 = 5 and b1 = - 1, find the sum of the series: %3D E(- 5an + 7bn) n=1…

A: We have to solve

Q: Let the series L3"242-" then:? n = 1

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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: Find the sum of the series. 1 + ח2,"(1-)5 Σ 22n + 1(2n n = 0 + 1)!

A: We have,   It is known that,

Q: How is the series 5 + 8 + 11 + ... +77 represented in summation notation? 25 ΟΣ(3q + 5) q=0 17 ΟΣ(4q…

A: Given Series is  5+8+11+........+77

Q: Prove that the sum of the series 1/2 , 1/4, 1/8, 1/16 .........to infinity

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Q: A. Find the value of the following series b. Σ=2 42-33-2n-3

A: Given ∑n=2∞4n-33-2n-3b.

Q: the sum to n terms of the series: 5 + 11 + 19 + 29 +

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Q: Find the sum of the series: 3n+2 5n-3 n=3

A: The given series is an infinte geometric series whose sum is S=a/1-r,r<1. See 2nd,3rd step.

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: 6. Find the sum of the series (-1)"-1 (-1)"72n 4" (2n)! nen n=1 2 3

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

Q: I need help :(

A: We have to find the sum of the series ∑n=0∞ 5-1nπ2n+132n+12n+1!. For this, we have to write the…

Q: Find 60 term of an A.P series 12,16,20..

A: The objective is to find  60 term of an A.P series 12,16,20..

Q: the summation notation for the series 0.3-0.9+2.7-8.1

A: The given summation is: S =0.3 - 0.9 + 2.7 -8.1  The above summation can also be written as,…

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: 08. The sequence { GT) }n-1 3n+2 37+1

A:

Q: Choose any that is an arithmetic series. 4+8+12+16+...+200 50 Σ(1-2) j=5 45 Σ(12 + 3) j=1 45 Σ 3* K…

A: Here we have to choose the arithmetic series. A series is said to be arithmetic series if difference…

Q: 4 5. Find the sum of the series 2 (2n + n³) n =1

A:

Q: 2 Suppose that E a, is an infinite series with partial sum SN = 6 – N2 ° n=1 10 16 What are the…

A: Here, the partial sum of the series ∑n=1∞an is given by: SN=6-2N2 where SN=∑ann=1N

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: (a) Find the sum of the series 4 – 3k+2 - 8k-1 k=0 (b) Find the value of r such that ) 3· r 2k+1 =…

A: For (a),     ∑k=0∞ 4-3k+28k+1=∑k=0∞ 48k+1-∑k=0∞ 3k+28k+1=4∑k=0∞ 18k+1-3∑k=0∞…

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: Find the sum of the infini:e series ; ab+x+ - + Q-= אab 2 24 120

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Q: The sum of the series n2n+1 -1)" 9n+1(2n)!

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Q: 100 а. 2" 3n 7 b. 2n=1 4n 100

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Q: Σ |(-1)"72n+1 (2n + 1)!22n+1° 2. Find the sum of the series n=1

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Q: (b) Use the result from (a) to find the eract sum of the infinite series 1 1 1 +. 16 4 9.

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Q: 1. Find the sum for the first 30th terms of the following series 2.4+4 6+6-8+.

A: Given the series is

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. 7(-1)"72n + 1 32n + 1(2n + 1)! n = 0

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Q: 2. Find the indicated term of a sequence. 4n %3D 2n -3

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Q: Write out the first 5 terms of the power series (3)" n! n=0

A: The solution for the above question is as shown below.

Q: Show that the series, x2 1+ x +- 2! x3 ... 3! 4!

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

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Q: Find the sum of the infinite series. 1 1 1 + 24 · 38 10 · 24 1 +... 52 · 66 38 · 52 (Use symbolic…

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Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.

Q: The sum of the series 2 3n-1 - 1 is given by n=1 6-1

A: Given series is an=3n-1-16n-1