Find the sum of the series 1 + 1/3 +1/9 + ... + 1/3^n−1 + ... Answer: .......

Q: What is the sum of the series corresponding to sequence: 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9,…

A: We have to find sum of the series:

Q: Find the sum of the series if possible: 2k 1 k 1 3k 2

A:

Q: How many terms of the series that is given below must be summed to estimate the sum of the series…

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Q: 9 k2 (k+1)2 ||

A: Given:=∑k=1∞9k2-9k+12

Q: Find the sum of the convergent series. 3+.

A: We need to evaluate the sum of the following convergent series 3+32+34+38+···········

Q: State where the power series is centered. Σ n = 0

A: We have to find center of power series

Q: The Interval of convergent for the series is: 4kk (a)[-4,4] (b)(-4,4] (c) [-4,4) (d)(-4,4)

A: The convergence of the series can be calculated using the convergence test. The ratio test is given…

Q: Find the sum of 10th term of the series (1) + (5+5) + (5 +5 +5°) + (5 + 5° + 5 + 5° +5°) +..

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Q: Determine how many terms should be used to estimate the sum of the entire series with an error of…

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Q: Find the sum of the first 31 terms of the following series, to the near 4, 11, 18, ...

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Q: Express as the sum of a power series: (5z + 6)(6z + 6) (3)"] 1/7 17

A: Using partial fractions:  x5x+66x+6=15x+6-16x+6                            =1/61--56x-1/61--x…

Q: Determine how many terms should be used to estimate the sum of the entire series with an error of…

A: Alternating seriese where error estimation theorem is used

Q: Find the sum of the convergent series. n = 0

A: Formula for finding sum of a convergent geometric series is,         sum=a1-r Where ,      a= first…

Q: Prove that the Sum of Convergent. Series is ungue

A: prove that sum of convergent series is unique.

Q: Find the first term of the series whose second and subsequent terms are, 8, 3, 0,-1, 0, ...

A: Given, the series whose second and subsequent terms are                         8, 3, 0, -1, 0, . .…

Q: Find the sum of the convergent series.

A: We have to find the sum of the convergent series: 8+6+92+278+................. up to infinite. So it…

Q: • Decide Calculate the sum. if this real series is Fonyergent or not Ornot. 9s well.

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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: Find the Sum of this series:

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Q: State where the power series is centered.

A: Given series: ∑n=1∞-1n2n-12nn!xn This series can be expanded as…

Q: 2. When can you say that a SERIES or SEQUENCE diverges? Prove it using mathematical approach.

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Q: If the n th partial sum of an infinite series is Sn = 4n2 − 3/ 3n2 + 4 , what is the sum of the…

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Q: Find the sum of the follow ing series as n → 0. n n n n + + n² +n° n°+1n² + 22 'n² +3?

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Q: estimate the sum of the series if n is given as 8

A: Given series∑n=1∞-1n-12n4 We have to calculate the sum for n=8 Now, ∑n=18-1n-12n4=…

Q: What are the first 5 terms of each defined sequence and give their associated series. Complete…

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Q: the first four terms to ximate the sum of the series:

A: Given,                ∑n=1∞1n2+1

Q: Soru 5 Find the sum of the given series if it converges. (-1)",2n 4 (2n–1)! n%3D2

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Q: n Σ 1 3 2 n = 0 8

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Q: When all the terms in a series are positive, is the sequence of partial sums an increasing sequence…

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Q: Find the sum of the series Σn(0.1)n from n=1 to n =8

A: Given data:   The given expression for the series is S=∑n=1n=8n0.1n.   The given expression can be…

Q: Σ is equal to n+1 alue of the partial sum of the infinite series ......

A: Given series is ∑n=1∞1n-1n+1

Q: n +3 2n + 1

A: We are given the series,                                . We need to check whether the series is…

Q: State where the power series is centered. Ση n = 0 1

A: We are going to find

Q: First four partial sums of the series, then find the limit as n approaches infinity if the sequence…

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Q: How can you estimate the error involved in approximating the sum of an alternating series with one…

A: The alternating series test:

Q: Calculate the sum of the series whose terms are 1, 2, 3, ..., 99.

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Q: Calculate the sum of the series 7 + ++ +

A: We need to evaluate the following sum 7+52+54+58+516+532+······

Q: Find the sum of the convergent series.

A: The given series is a geometric series with common ratio less than one. So we can use formula for…

Q: n=1 ,2n TO

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Q: Find the sum of the series. Summation of (7^n)/(3^n)n! from 0 to infinity

A: To find the sum of the series.

Q: What is the formula for the nth partial sum of the series? If the series is convergent, what is the…

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Q: Estimate the error in using the partial sum of 50 terms of the series

A: Error  ≤ 0.0000000032.

Q: Find the sum of the convergent series. Σ

A: The given convergent series is, ∑n=0∞-47n To find its sum.

Q: Find the sum of the series.

A: The series is:

Q: Find the sum of the convergent series.

A: Given series : ∑n=0∞ -15n The given series is ∑n=0∞ -15n=1-15+125-1125+...... The given series is…

Q: Determine the number of terms required to approximate the sum of the series with an error of less…

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Q: What does it mean for infinite series to diverge?

A: Given: Infinite series to diverge:

Q: 4. Find the sum that the series 1 will converge. 27 -19

A: Given Information :

Q: Determine how many terms should be used to estimate the sum of the entire series with an error of…

A: Use the  Alternating Series Estimation Theorem and solve the problem.