4. An awesome rubber object is dropped from a height of h metres and hits the floor. It rebounds to a height of ah where a e (0, 1). Suppose this repeats infinitely. Let s be the length this rubber object has travelled. Find an expression for s using an appropriate infinite series. Note: your final answer should be in terms of h and a, but not an infinite series.

Q: 8. Find the sum of the series 5 if it exists. If no sum, write diverges on the blank provided. k=0…

A: Explanation of the answer is as follows

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A:

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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:

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A: Given query is to find sequence converging or diverging m

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A: We find interval of convergence

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A: Series and sequence

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A:

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A:

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A:

Q: 1 a) Starting with the fact that x". ', express the function (45 + x) In(45 + x) as a power series…

A: We use the term by term integration

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A: The general form of an infinite geometric series is: a + ar + ar2 + ar3 + ..... Here, a is the first…

Q: 3 accurate to ind the smallest number n of terms needed to obtain an approximation of the series…

A: Given the series ∑k=1∞3k5

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A:

Q: Which amongst the following is required to find mode in continuous series?

A: Let f1 be the highest frequency number fo be the frequency just preceding highest frequency number.…

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A: An infinite geometric series converges for -1 &lt; r &lt; 1, for all other values of r, it diverges,…

Q: 4. For the series Σ=1+()", does it converge and if so what does it converge to? * n²

A: We have to check that series 1/2*(2/5)n  where n=1 to infinity. Is convergent or divergent.

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

A:

Q: Find all the values of x such that the given series would converge. (x – 8)" 8 n=1 Answer: Note:…

A: Explanation of answer is as follows:

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: 1 Find the value of x for which the series +++ .… converges and express the sum as a function of x.

A:

Q: 1. The mathematician Srinivasa Ramanujan found an infinite series that can be used to generate a…

A: import math s=0 k=0 term=1 while term&gt;1e-15:…

Q: 3) Find the sum of the series (x-8) as a function of x on the domain, and say what the domain is.…

A:

Q: If it is known that lim, ap =0, that is the k term of a series goes to zero as k goes to infinity.…

A: That's easy. Have a great day!!!

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: Determine whether the statement, 'The sum of the geometric series 1/2 + 1/4 + 1/8 + ..... + 1/512…

A: Given: Geometric series is 12+14+18+⋯⋯+1512 Here, first term is a=12 Common ratio, r=1412=12 We know…

Q: Find the sum of the infinite geometric series if it exists.1 - 0.1 + 0.01 - 0.001+....

A: Given: 1-0.1+0.01-0.001+...

Q: For what values of x do the power series x" converge. n=1

A: The given power series is ∑n=1∞1+1nnxn. Consider an=1+1nnxn By using root test,…

Q: D. Estimate 2 (-1)" / (3ª + 12) to within an accuracy of 0.01. (Make sure to verify the series meets…

A: This is a problem of sequence and series.

Q: 1 1 hen write this function a power series centered at 0: | (43 + x)In(43 +x)

A: Given function is,  fx=43+xln43+x.       ......1 Taylor series expansion: Taylor series expansion of…

Q: 9.3 For each series, is it divergent or convergent? Give reasons. In n ( 6) Σ n=1 (b) sin(n) n3/2…

A: use the comparison test to check the convergence of both series:-

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: 10) Show that the series is convergent. How many terms of the series d we need to add in order to…

A: Given: ∑n=1∞-1n-1ne-n

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A:

Q: Consider the series n Σ 3n + 10 n=1 Determine whether the series converges, and if it converges,…

A: When the limit of function lies between 0 to 1 , then the given function is convergent and when the…

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Q: E 2 > 2 ke-k converges or diverges Determine whether the series

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Q: 1 Use the identity Σ to express the function as a geometric series in the indicated term. %3D 1 - y…

A:

Q: 1 3. How many terms of the convergent p-series k=1² must be summed to obtain an approximation that…

A: We have to find no. of terms of the convergent p series.

Q: Suppose Ea, and Eb, are series with positive terms and Eb, is known to be divergent. If a, > b, for…

A:

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

A:

Q: I. Determine whether the infinite series is convergent or divergent. 7. E(-1)" 1+00 n2 8. Σ(-1)" "…

A:

Q: 3. For the SERIES 2e ,determine whether it converges or diverges. If it converges, find n=0 the sum.

A:

Q: Find the smallest value of x for which the series (x + 46)" 2'n(n) is conditionally convergent.…

A: Given series is ∑n=2∞(x+46)n2ln(n)

Q: 1. Find the first four terms and the (n + 1)th term of the series whose nth term is: (-1)*-1, (2n)!

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

Q: Which of the following is the correct formula for the sum of the finite geometric series below? 3 3…

A: Sum of finite geometric series =a(1-r^n)/1-r When r&lt;1.

Q: 3. Determine whether each geometric series converges. If the series 7n+1 2n converges, find the sum.…

A: Let's find.

Q: 8.1 Define what it means for a series E an %3D to converge.

A: We will use the concept of converging series. According to our policy, we can only answer one…

Q: The series 4 + 12 + 36 + ·.· has no limiting sum because r > 1. Nevertheless, substitution into the…

A: Given series is