The sum Sn of the first n terms of a series is given by S, ="(3n + 1). Show that the series is an arithmetic series

Q: Determine the sum of the series 2 n(n + 2) n=1 if possible. (If the series diverges, enter…

A: Summation of series using method of difference

Q: The sum of the series (if it exist) is Ln=1 +11n+30

A: Given, ∑n=1∞1n2+11n+30 To evaluate sum of series if it exists

Q: Find an example of two sequences (an)neN and (bn)neN such that both sequences Ei=19 and ₁=1b;…

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Q: B/ Find the values of x that make the series (x+3)-1 convergent

A: Power Series: A series of the form  ∑n=1∞anxn=a0+a1x+a2x2+... where a0, a1, a2, ..., etc. are…

Q: Find the sum of the series Σx7n-2/n! from 0 to infinity

A: The objective is to find the sum of the series ∑n=0∞x7n-2n!

Q: The nth term of the series .. IS: Select one: a. n an %3D n+1 O . 1 an 0,-(-) n+1 OC. an = (1-1/n)

A: Proceed as shown below...

Q: Determine how many terms of the following convergent series must be summed to be sure that the…

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Q: Find the sum of the series Σ 3n(x-3)n/(n+3)! from n=1 to infinity

A: To compute: ∑n=1∞3nx-3nn+3! ∑n=1∞3nx-3nn+3!=∑n=1∞3x-9nn+3!∑n=1∞3x-9nn+3!=∑n=1∞3x-9n+33x-93n+3!Shift…

Q: Find x such thatEx+2)-n = 4. (Hint: Use the formula for the sum of a geometric series.) n=0 X =

A: Series and sequence

Q: Write the first four terms of a power series with coefficients c0, c1, c2, and c3 centered at 0.

A: The coefficient of the first four terms of the power series is ck with centered is 0 for k=0,1,2,3.…

Q: The exact value of the series is discovered by /-

A: Consider the series

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: Find the Generating function for the sequence 1,3,9,27,81,. Also find for which value the series…

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Q: Find the sum of the series. e -8x² Σ (−1)n 87x6n n = 0 n! X

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Q: write out the first eight terms of each series toshow how the series starts. Then find the sum of…

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Q: ) Find the interval of conver gence of the power Series * (4)" (n-2)_ (x -2)^ | n 2" n=3

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Q: n of a series with its own lagged values is called

A: The correlation of a series with its own lagged value is called as autocorrelation

Q: 2n-1 n²(n+1)

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Q: Express the given power series as a series with generic term x". 00 Σ n+3 n+3 n=8 Σ

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Q: 3. 5n3 +6 n=0

A: We have to find the given series which is convergent or not. ∑n=0∞3n3+7n5n3+6 It is known that if…

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

A: Use sum of formula of infinite term of gp

Q: Find the sum of 100 terms of the given series 0.6,1.7,2.8...... to 100 terms

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Q: Given that the series converges, find the sum of the series (see picture)

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Q: Find the sum of the series (-1)"-1 (n + 1)ni"-1 n=1

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Q: 1. (-1 )-1 ( 2n )! 2. (-1 )n-1 2n – 1 n (n+ 2) 2. (- 1 )"1-

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Q: Find the sum of the series. n! n- 0

A: Given series is ∑n=0∞-1n6nx2nn!                 (i) To find the sum of the given series (i).  Now,…

Q: Show that the series is convergent. How many terms of the series do we need to add in order to find…

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Q: Find the sum of the series, if it converges. Otherwise, enter DNE. Σ (-8)"-1 n=1

A: We have to find sum

Q: If aN is the nth digit in the decimal expression of 1/3, is the series convergent or divergent?…

A: According to the given information, An is the nth digit in the decimal expression. So, for the…

Q: Find the sum of the series from n=2 to ♾ of.  6/(n^2+4n+3)

A: The given series is: ∑n=2∞ 6n2+4n+3

Q: Find the sum of the series as a function of x.

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Q: Find the positive values of p for which the series converges. 1 9) Σ n(Inn)" n=2

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Q: Consider the following series. Vn + 5 n2 n = 1 On your paper, re-right the series of the sum of two…

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Q: . Find the 31 st term of a series that has an nth term given by (10+2n)

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Q: Find the values of p for which the series converges. In n n= Answer (in interval notation):

A: Explanation of the answer is as follows

Q: Write the Maclaurin's series up to 5 terms of the function 1- 8x

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Q: How many terms of the series (-1)" 1+2" are needed to compute the sum of the series with an error…

A: By Alternating series estimation series test : s=∑n=1∞(-1)nbn        1)  bn+1≤bn2)  limn→∞ bn=0Then…

Q: (1+x)n

A: We can solve this as follows:

Q: Estimate the value of the sum of series, s = En 00 2n=0 (-1)" n! > to within an error of 0.0002.

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Q: Find the sum of the first 10 terms of the series. A (n) = 5n – 2 S10

A: Finding S10

Q: Use the estimate |RN|< bN+1 to find the smallest value of N that guarantees the sum of 1 differs…

A: Given that, ∑n=1∞(-1)n+11n+3 Here N is the sum of first n terms, N=limn→∞an+1an Here an=(-1)n+11n+3

Q: Find the sum of the series: n! n=0

A: Given series ∑n=0∞x6n-3n! Let us rewrite the given series as follows ∑n=0∞x6n-3n!=∑n=0∞x6n.x-3n!…

Q: How many terms of the series (-1)" 1 + 2" n=1 are needed to compute the sum of the series with an…

A: To find the number of term such that the error is less than 0.001 .

Q: How many terms of the series -1)" 1+2" are needed to compute the sum of the series with an error…

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Q: Select all the series that converge. 1 E(-1)"-1, Inn n=3

A: We have to find out the convergent series.

Q: What is the sum of the series (1)/(n2-1) if n starts at 2 and goes to infinity?

A: To find the sum of the series  ∑n=2∞1n2-1

Q: Consider the series , ark1, a 0. Then if r < 1, the series converges to

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Q: Write an equivalent series with the index of summation beginning at n = 1. E(-1)" + (n + 1)Jox" n =0…

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Q: Given the series: 2 k=1 does this series converge

A: Answer and explanation is given below

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.