
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Use the approach in Gauss’s problem to find the following sums of arithmetic sequences (do not use formulas):1+3+5+7+…+1001
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- a =(−1)²¹ (n − 10)₂ - What is the 9th term of the sequence narrow_forwardIf you were to shade in a n × n square on graph paper, you could do it the boring way with sides parallel to the edge of the paper) or the interesting way, as illustrated below: The interesting thing here, is that a 3 x 3 square now has area 13. Our goal is the find a formula for the area of a n × n (diagonal) square. (a) Write out the first few terms of the sequence of areas (assume a1, a-5, etc) Is the sequence arithmetic or geometric? If not, is it the sequence of partial sums of an arithmetic or geometric sequence? Explain why your answer is correct, referring to the diagonal squares (b) Use your results from part (a) to find a closed formula for the sequence. Show your work. Note, while there are lots of ways to find a closed formula here, you should use partial sums specifically. 6 Bonus: For the sequenc n question 5, find the closed formula in as many interesting ways as you can.arrow_forwardUse the approach in Gauss’s Problem to find the following sums of arithmetic sequences. 881+872+863+854+....8arrow_forward
- Use the approach in Gauss's Problem to find the following sums of arithmetic sequences. 293+290+287+284+..+2arrow_forwardFor the sequence defined by: a₁ = 8 an = Find: 3 an-1 2 a₂ = 0 -1.625 Round your answer to 3 decimal places as needed. a3 = 0 -3.846 Round your answer to 3 decimal places as needed, but do not use the rounded answer for the previous term in your calculation. a4 = -2.78 Round your answer to 3 decimal places as needed, but do not use the rounded answer for the previous term in your calculation.arrow_forwardIn an arithmetic sequence t(6)=33 and t(41) = 138 what is t(0)?arrow_forward
- Let (an) and (bn) be sequences of real numbers with the following properties:arrow_forwardUse the approach in Gauss's Problem to find the following sums of arithmetic sequences. A. 1+2+3+4+...+1001arrow_forwardFor the sequence an = an–1+ an– 2 and a1 = 2, a2 = 3, %3D its first term is its second term is its third term is its fourth term is its fifth term isarrow_forward
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