Find the sum of An of the arithmetic series that satisfy the given condition n= 7, a1 = 2, d = 7. Give the answer first then Show your solutions.

Q: In  the given equation as folows , write an equivalent series with the index of summation beginning…

A: Definition used -                                   ∑n=0∞an=a0+∑n=1∞an

Q: А. Σ 5n –1 n=1

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Q: he sum of the first " n" terms of the series is 2n + 3 + x. Find the seventh term.

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Q: The sum to infinity of a geometric series is five times the first term. Find the common ratio. r=

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Q: 4 Find the sum of the convergent series TI(n +2) Tm1

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Q: Find the sum of the infinite series, if it exists. -16 -64 32 8, , 5, 27· 3 Enter the sum as a…

A: The given infinite series,8, -163, 329, -6427,.......

Q: 3" 14" n=3 S

A: Given data is: ∑n=3∞3n14n

Q: determine the number of term n in each geometric series ex:1 a1=-2, r=2, Sn=-14 ex2: a1=2, r=2,…

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Q: By differentioating the series G1)" T find the exact value of (-1)".3u

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Q: Illustrate how to use a known series to determine the exact value of (-1)" (n)4n (2n)! n=0

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Q: determine the number of term n in each geometric series ex:1 a1=-2, r=2, Sn=-14 ex2: a1=2, r=2,…

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Q: is a constant. . If |r| < 1, the sum of the geometric series E ark-1 is k=1

A: Known fact: ∑k=0∞ a rk=a1-r       provided r&lt;1.

Q: Use the fact that Σ nxn-1 to find the sum of each series. (1 - x)2 in (a) n = 1 ΗΣ E(9)'-C (b)

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Q: The sum of the series Σ 1 is: 2" n=1

A: Given that: ∑n=1∞12n

Q: The sum to infinity of a geometric series is 60. If its first term is 80, find the common ratio. А.…

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Q: The sum of a geometric series of six terms with ratio 2 is –126. Find the first term. 126 31 43 © 31…

A: Solution: Consider the given geometric series having ratio r = 2 and sum of six-term (n = 6) is =…

Q: Find the values of p for which the series is convergent. (Enter your answer as an inequality.) 00 9.…

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Q: Find the sum of Gn of the Geometric series that satisfies the given conditions. n = 6, a1 = 5,r= 4…

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Q: find the solution of the expression y(x) with the power Series in x=0?

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Q: Find the first term for the geometric series described: Sn=484 an=324 r=3

A: Recall: Sum of the n-terms of the geometric series , Sn = a( 1-rn) /(1-r)    ; where a is the first…

Q: Find the sum of the series, if it converges. Otherwise, enter DNE. 8 Σ (-3)" w=1

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Q: Find the values of p for which the series is convergent. (Enter your answer as an inequality.) 7…

A: See the attachment

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

A: we have to show that given sum of n term of series is an arithmetic series   According our…

Q: The power series x +......... can be expressed as 5 3

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Q: use thE formula for the sum of a geometric series to find the sum or state that the series diverges

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Q: Find the sum of the series, if it converges. Otherwise, enter DNE. (VII)" n=0

A: We can write given series as: ∑n=0∞111n2∑n=0∞11-n2 It is an infinite geometric series with the first…

Q: The sum of the first three terms of a geometric series is 52, and the common ratio is r = 3. Find…

A: Given: The sum of the first three terms of a geometric series is 52 S3=52 Common ratio is r = 3…

Q: use thE formula for the sum of a geometric series to find the sum or state that the series diverges

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Q: The sum of the series 5 + is given by A. and 27 is given by B njo

A: sum of infinite geometric series:a+ar+ar2+····=a1-r where r&lt;1-----i

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

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Q: Find the sum of the series below. 56n n=1 (2n – 1) (2n + 1)? The sum of the series is

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Q: By power series, solve the ODE y' - 2xy = 0.

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Q: Find the sum of each series

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Q: Write the given decimal as an infinite series, then find the sum of the series, and finally, use the…

A: The sum of the infinite geometric series with first term a and common ratio r is given by…

Q: (1+x)n

A: We can solve this as follows:

Q: Determine the least number of terms one would have to take in the alternating series (-1)k-1 k-4 k=1…

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Q: Find the sum of the series and put the result in simplest form.

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Q: Find the sum of the series, if it converges. Otherwise, enter DNE. бn? — 3 n2 +1 n=1

A: A necessary condition for convergence of a infinite series ∑n=1∞un  is limn→∞ un =0. Now to find the…

Q: Find the sum of n terms of the series whose nth term is (i) 2n? - 3n + 5 (ii)n? + 2"

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Q: To find the sum of the series 2 express y as a geometric series, differentiate both sides of the…

A: Given problem is :

Q: The second term of a geometric series is 4 and its sum to infinity is 18. a) Prove that the common…

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Q: The first three terms of a geometric series are 2x, x-8, and 2x+5 respectively. Find the possible…

A: If a, b, c are in geometric progression, then it can be written that ab=bc .

Q: Find the sum of series, An= {(1/n)-(1/(n+1))}. What kind of series is this?

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

A: We find the sum of the series by the sum of the known series.  We know that (1+x) -1 =…

Q: Find the sum of the series n=3 gn

A: Given: Series ∑n=3∞2n5n

Q: 00 5h 12 n=2

A: Here, the given series is  ∑n=2∞5n12n

Q: Find the sum of the series whose terms are an=1/5^n. What kind of series is this?

A: Series