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: Problem 4. Part (a) Part (b) 5ln(3-x) = 4 Do both parts. Write the sum using sigma notation:…

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Q: nd the following sum: 2 + 4 + 6 + 8 + ... + 88 using Gauss' method. Show all ste

A: To find the below sum using the Gauss' method. 2+4+6+8+...+88

Q: 4. Consider the sequence 8 1 {2(k+3 (2(k+3)) k=1 rewrite the sequence from j-5

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Q: For the sequence 2, 4, 8, 16 .. ., give a formula for its nth term:

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Q: Write the first four terms of the of the sequence tn 2tn-1 + 4 where t₁ = 5 P

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Q: 27 3. What is the formula for the nth term of the sequence: 8,-6, , 8. ...

A: The given sequence is 8, -6, 92, -278

Q: Sequence hWith frst tem 7, and las term 7/729.

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Q: 3n - 1 an = n! a1 a2 az a 4 as

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Q: Q1. find the sum by adding each term together. (3i + 2) i=1 1 k2 + 1 k=0

A: ∑i=163i+2 ∑k=041k2+1 ∑ck=07

Q: 1 B. E 2n +1 2n +3 n=1

A: Solution of the above series is

Q: (a) Place the digits 7, 9, 10, 11, and 12 in the circles to make the sums across and vertically…

A: The digits 7, 9, 10, 11, and 12 are given.a) Arrange the numbers such that the horizontal (the sum…

Q: A sequence built from the digits 1, 2, 3 is safe if the digit 3 only appears immediately after the…

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Q: Use iteration to guess an explicit formula for the = 2dr-1 + 3, for each integer k > 2 if d = 2…

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Q: 14. In a sequence of three squares, the second and third squares are symmetrically in- scribed…

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Q: For the sequence defined by: a1 = 3 an+1 Find: a2 = a3 = a4= 5 an +3

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Q: 2. Find a formula for the sequence given by In+1 = 4xn – 5xn-1+ 2xn-2 n > 2, 5xn-1+ 2xn-2 n> 2, with…

A: We have  xn+1=4xn-5xn-1+2xn-2   n≥2    ...(i)x0=2,x1=7  and x2=15characteristic equation of (i) is…

Q: If term one = 93.19 and term 8 = 870.02 Show geometric progression for all 8 terms with working…

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Q: 5. Find the sum: Σ n²+4n + 3

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Q: 2. Find a formula for the sequence given by Xn+1 4.xn - 5xn-1 + 2xn-2 n 2 2, with xo = 2, x1 = 7 and…

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Q: The fourth term is 12 and the seventh term is 32 Find the first and nth terms..

A: Find first and nth term