Problem : Using Ratio test, determine the nature of the series : 9n

Q: write the ex pression? オ2 n2 0 asa series whose generic term involves X

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Q: The local truncation error is the error made at a single step due to the truncation of the series…

A: The local truncation error (LTE) of a numerical method is an estimate of the error introduced in a…

Q: State what test you are using and show the given series satisfies the assumption for the test.…

A: ROOT TEST:    Let ∑n=1∞an  be the positive term series and let  limn→∞ ann= L.Then,…

Q: (3x – 3)" is a power series centred at Answer:

A: Given that: ∑n=0∞(3x-3)n

Q: Write the power series for  (1 + x)k  in terms of binomial coefficients.

A: The binomial theorem is given below:

Q: What test is advisable if a series involves a factorial term?

A: Let the series involves a fractional term ,

Q: Suastion 2 8, と what is the power Series expor sion と 1. -()け a)3 と 3 と-○ c)を

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Q: How do you use the Alternating Series Estimation Theorem (ASET) to determine how many terms would be…

A: Given series, ∑n=1∞-1nn4 Using Alternating Series Estimation Theorem (ASET) to find the terms that…

Q: 28. The value of In (2) can be calculated by the alternating harmonic series. In (2)-1-+-+ Using the…

A: Here is the solution:

Q: Can the value of a series be determined using the Root Test or theRatio Test?

A: No, we cannot determine the value of the series using the root or ratio test. It can be only used to…

Q: Consider the series An where n=1 (n + 8)! en-1 /n +1 an

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Q: Discuss the idea of power series method and prove that y`=2xy

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Q: Find the sum of the given series to the accuracy IerrorI < 0.01. Explain how you estimate the…

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Q: By suitably manipulating the geometric series E xn -1 < x < 1, you can calculate 1-x n=0 the sum of…

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

A: Consider the series

Q: By using ratio test the series E=1n!(-) is

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Q: 35, (.5n + 307) n=1

A: ∑n=135 (0.5n+307)=∑n=135 0.5n+∑n=135 307  =0.5∑n=135 n+307∑n=135 1

Q: M118(-65) -1

A: ∑n=1∞118-0.65n-1

Q: The value of p for the series En=1n! e¯n by using ratio test is 2 O 8.

A: Ratio Test: Let ∑n=1∞un be a given series such that limn→∞un+1un=ρ Then the series converges iff…

Q: 2" +1 Ln=0 3"

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Q: The formula for the sum of the first n terms of a geometric series is given by  Sn =_______(r ≠ 1).

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Q: While determining the nature of the series n! using Ratio test, the value of L is compared with 2n

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Q: State where the power series is centered. Σ (-1)"(x – 77)5n (5n)! n = 0

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Q: Explain why the magnitude of the remainder in an alternating series(with terms that are…

A: The magnitude of the remainder in an alternating series (with terms that are nonincreasing in…

Q: - , How many terms of the series do we need to add in order to find the sum to the inaicated…

A: The approximation of a series is obtained by substituting large values of the variable. Very large…

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

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Q: Given the power series expression Σ 4 n x" + 2 n (n - 2) x" n = 0 n = 3

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Q: The student is confused, because every term in the original series is positive, hence the series…

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Q: While determining the nature of the series n! using Ratio test, the value of L is 3n n=0 compared…

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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: >n Cnxn-2 n=4 26°C Güneşli

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Q: While determining the nature of the series n! , using Ratio test, the value of L is 6n n=0 compared…

A: To find the value of L using ratio test

Q: State where the power series is centered. 00 (-1)"(x – 5x)8n Σ n = 0 (8n)!

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Q: (1+x)n

A: We can solve this as follows:

Q: 28. The value of In (2) can be calculated by the alternating harmonic series. In (2)-1-+-+ Using the…

A: This is a question of infinite series.

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: Σ n+2 n=1

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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…

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

A: We are asked to find the sum of the series.

Q: п (х-2)" b) Σ 3 п n=1

A: Given that ∑n=1∞x-2nn3we have to find centered of power series

Q: Σ Find the sum of the series correct to 3 decimal places. n3 n = 1 1.186

A: Given the series∑n=1∞1n3

Q: State where the power series is centered. (-1)"(9n – 1) 9 n! n= 1

A:

Q: Write the general formula for following alternating series in the form > an. n=1 5 5 - ... 8 10 11…

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Q: Solve using Power Series Centred Around Zero. (X²+1) y" - 4XỲ +6y=(X² +15²³

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

A: A power series centred at (or about) x=c is a series of terms such that all terms are non-negative…

Q: What is the sum of the series below if x = 0.2. 1+ 4x + 16x2 + 64x3 + ...

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Q: n! While determining the nature of the series 8n n=0 using Ratio test, the value of L is compared…

A: the series is divergent by limit test.see 2nd step for solution.

Q: State where the power series is centered. Σ (-1)"(x – 47)6n (6n)! n = 0

A:

Q: n! While determining the nature of the series , using Ratio test, the value of L is compared with 2n…

A: The series is ∑n=0∞ n!2n Ratio test: Let the power series is ∑n=0∞ an Define L=limn→∞an+1an If l…