1. Suppose that Achilles runs 10 times as fast as the tortoise and that Achilles runs 10 yards a second. Suppose that the initial distance between Achilles and the tortoise is 100 yards. Then Achilles runs successively 100 yards, 10 yards, 1 yard, and so on. Find the total number of yards Achilles must travel in order to catch his competitor and find the total number of yards the tortoise must travel, by using the geometric series that you learned in Calculus. 1 10 yard,

Q: Find the sum of a geometric series with the given information an = 192 , n = 7, r = 2

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Q: Evaluate the geometric series or state that it diverges.

A: Common ratio= r= -0.15  So, |r|=|-0.15|=0.15 < 1 So this series will converge

Q: Find the sum of the terms of a series 2n-1 2"

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Q: Find the infinite sum, if it exists for this series: -2 + (0.5) + (– 0.125) + · · ..

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Q: The 3rd term of an arithmetic series is 34 and the 17th term is –8. Find the sum of the first 20…

A: As we know that n-th term of an arithmetic series is    a+n-1d, where a = 1st term and d= difference…

Q: 9. find the of the geometric series. sum if possible. 3(2)"-! nil

A: We have to find sum

Q: Find the sum of the finite geometric series 3+3/2 +1+3-1/2 + ...+3-21.

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Q: Find the sum of the infinite geometric series defined by 4(0.5)"-1 O None of the choices O 1 O 4 O 8

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

A: Given: ∑ an  and ∑ bn are series with positive terms and ∑ bn  is known to be divergent. a) If…

Q: The great Swiss mathematician Leonhard Euler sometimes reached incorrect conclusions in his…

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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: I know to find the sum in an infinite geometric series using S=1/1-r, that it converges if -1<r<1,…

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

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: Find the sum of the infinite geometric series if it exists.

A: We have to find the sum of infinite geometric series: 2-2+8-4+.... We know that if we have infinite…

Q: Find the sum of the infinite geometric series:

A: Given: S=3+2+43+89+................. We know that sumS of infinite geometric series is given by…

Q: Use the estimate R₁ ≤ b+ 1 to a value of N that guarantees that the sum of the first N terms of the…

A: answer is in next step . please give a like !!

Q: Find the infinite sum, if it exists for this series: - 2+ (0.4) +(- 0.08) + · ....

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Q: Find the sum of the first 60 terms of the series whose terms are defined by: an = 8+ (n – 1) (-3)…

A: We use concept of arithmetric progression.

Q: Find the sum of the infinite geometric series. Σ 2 5.6 · 0.5"-1 n = 1 S =

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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: Find the infinite sum, if it exists for this series: – 2 + (1) +(- 0.5) + ..

A:

Q: The sum of the first three terms of a geometric series, whose first term is 2 and whose common ratio…

A: We have to apply the formula of Sn(sum of n term of geometric series)

Q: If we only add six terms of the series estimate how far off (at most) we (r – 2)(x + 3)' could be…

A: Given Series is ∑x=3∞1x-2(x+3).We have to estimate how far off we could be from the actual sum.

Q: 2) Explain, in your own words, what it means for an infinite series to converge.

A: We have to explain the meaning of convergene of a infinite series.

Q: n Σ 1 3 2 n = 0 8

A:

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: Find the sum of the infinite geometric series.

A: For | r | &lt;1 S∞=a11-r

Q: If the series 1(-1)" 2 were approximated using its first k terms, what would be the smallest number…

A: We have to find the smallest number of k such that the error bound would guarantee an error of not…

Q: Find the sum of the first 18 terms of a geometric series if the first term is 1 and r= 2.

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Q: Make up a geometric series Σarn-1 that converges to the number5 if a = 13/2.

A: Given:

Q: what is the sum of geometric series for which a=2, n=5, and an=35?

A:

Q: Find the sum of the infinite series, if it exists 1, 2, 4, 8,.. 16

A: The sum of an infinite geometric series (GP) is given by , where a is the first term of the series…

Q: 4. Find the sum of the geometric series 3-3/2+3/4-3/8+3/16 - ..

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Q: 7n2 + 2n (b) Does the series, converge or diverge? If it converges, what does 3+11n2 + 5n n=1 it…

A:

Q: Find the sum of the infinite geometric series if it exists.1.5 + 0.015 + 0.00015 +....

A: G.P SeriesA Series, in which each term is found by multiplying the preivous term by a fixed…

Q: Find the exact sum of the series 1 - 1 + (1/2!) - (1/3!) + (1/4!) - (1/5!) + (1/6!) - ...

A: Topic:- sequence and series

Q: Write an equivalent series with the index of summation beginning at n = 1.

A: ∑n=2∞x3n-12n-1!

Q: Evaluate the geometric series or state that it diverges.

A: Given ∑m=2∞52m. Expanding the series, we get ∑m=2∞52m=522+523+524+⋯⋯ Given series is geometric…

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

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

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

A:

Q: B) TV manufacturer plans to increase his output by 5% each month. If he is now producing 300 TVs per…

A:

Q: Find the sum of the geometric series. (3 Σ 4 n = 1

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Q: Find the sum of the series whose terms are an=(1/n)-(1/(n+1)). What kind of series is this?

A: topic -series and its summation

Q: The sum of the series n-n+1 n! is

A: Solution : To find, ∑n=0∞n2-n+1n! Taylor expansion of ex around 0 ex=∑n=0∞xnn! put x=1; e=∑n=0∞1n!

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

A: Series

Q: Find the sum of the series Σ /n+4 n = 1

A: First operate the given sum on both terms and then calculate the sum.