Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula 1 2/2 (4n)!(1103 + 26390n) - = 9801 (n!)*3964n TT n=0 William Gosper used this series in 1985 to compute the first 17 million digits of T. (a) Verify that the series is convergent.

Q: Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula 1 2 /2 (4n)!(1103 +…

A: given a formula 1π=229801∑n=0∞4n!1103+26390nn!43964n (a) to verify that the series is  convergent…

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Q: Verify that the infinite series diverges.

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Q: Show that the series below is convergent. nn (2п)! n=1

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Q: n4 /ant lim n %3D n00 -

A: Root Test : For a series ∑n=1∞an If limn→∞|an|n<1, then ∑n=1∞an converges. If limn→∞|an|n>1,…

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Q: If a given series converges and each term is positive, then the square of the series also converges.

A: The statement is true.

Q: Determine whether the series converges or diverges.

A:

Q: What is the largest value of x for which the series (x – 11)" - n°5" n=1 is absolutely convergent?

A: This is a problem of series and sum calculation. Based on the formula and concept we will answer the…

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Q: Find the interval of convergence for the series E- nx" in=D

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Q: Use any method to determine whether the series converge. (a) 11k k=1 8.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine whether the series converges, and if so find its sum. 4k+2 Σ k=1

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Q: Use an appropriate test to determine whether the series converges. 2(k!)4 9(4k)! Σ k=1 By the this…

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Q: Verify that the infinite series diverges.

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Q: Apply the Ratio Test to show whether the infinite series is convergent or divergent n! Σ (-2)"

A: Given problem:-

Q: Use an appropriate test to determine whether the series converges. 00 k3 Σ k5 +5 k =1 By the this…

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Q: 8 Σ η=1 1 3Vn + n η

A: Calculate the limit of the given term as n reaches infinity.

Q: Suppose that a is a number such that -9 an+1 -3)2n+1 n=0 convergent or divergent? If the series is…

A: given sequence is                                                      ∑n=0∞an+1(-3)2n+1

Q: 00 (4-x)"· /n+5 9n · 7" n=1

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Q: (-1)"-1 n=1

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Q: 00 (-1)" Ln-1 n п — n=2

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Q: Determine whether the series converges or diverges. 8 Σ sin() n=1

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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…

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Q: Does the series from 1 to  infinity of (n^2)e^(-n^3) converge or diverge?

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Q: Find a power series that converges only for x in [2, 6).

A: THEOREM 1 Radius of Convergence : Every power series                         F(x)=∑n=0∞ an(x-c)has a…

Q: Suppose that the power series ) Cn(x – 1)" converges when x = -2 and diverges when n=0 x = 6. (a)…

A: The power series ∑n=0∞cnx-1n converges when x = -2 and diverges when x = 6. We have to find the…

Q: Determine whether this series converges or diverges. 1 n=2 n° – n²

A: Explanation of the answer is as follows

Q: Determine whether the series converges or diverges Σ ln(n/3n+1) from n=1 to infinity

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Q: Determine whether the series is convergent or divergent. Ine пе n-1

A: According to the given information, it is required to check whether the given series is convergent…

Q: Determine whether the series converges or diverges.

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Q: Find the radius of convergence and interval of convergence of the series. Σ 3n! n=1

A: see 2nd step

Q: determine whether the series converges or diverges.

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Q: Show that the series whose nth term is n2 An 2n - 1 is convergent.

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Q: Apply the root test to prove that this series converges absolutely: (- 1)"*' 2" n=1

A: Ratio Testlimn→∞|an|n=LIf L<1,then absolutely convergent.If L>1 ,then Divergent.If L=1 then no…

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Q: Verify that the infinite series diverges.

A: Given series, ∑n=1∞an=∑n=1∞n+1!5n!

Q: Find the smallest number n of terms needed to obtain an approximation of the series accurate to…

A: The general form of the series is ∑n=1∞-1n+1an. Comparing with the given series ∑k=1∞2k3,an=2n3 To…

Q: . The series V8 (4n) !(1103 + 26390n) 1 9801 (n!)*3964n was discovered by Ramanujan in the early…

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Q: (-3)"x" n! n=1

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Q: State what it means for a series to be absolutely convergent. As well, if >Ja, converg * (2n +1) 1..…

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Q: 1 n2 п-1 1 1 n 00 (-1)" п-1

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Q: 2k+5 ニ k=1

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Q: Come up with a power series (not necessarily centered at 0) that converges only at x = 153 but…

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Q: En'e-n³ n=1

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Q: Determine whether the series converges or diverges.

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Q: Determine whether the series is convergent or divergent. 00 In(n) n = 1

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Q: 27 1 2n + 1 n=1

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.