Consider a series of diagonal squares, constructed as shown below: On=1 n = 2 n=D3 n=4 Note that the "3 x 3" square has area 13, and the "4 x 4" square has area 25. Our goal is the find a formula for the area of an "nx n (diagonal) square. (a) Write out the first six terms of the sequence of areas (assume aj = 1, ag = 5, etc). (b) Use your results from part (a) to find a closed formula for the sequence. Show your work. Hint: A.
Consider a series of diagonal squares, constructed as shown below: On=1 n = 2 n=D3 n=4 Note that the "3 x 3" square has area 13, and the "4 x 4" square has area 25. Our goal is the find a formula for the area of an "nx n (diagonal) square. (a) Write out the first six terms of the sequence of areas (assume aj = 1, ag = 5, etc). (b) Use your results from part (a) to find a closed formula for the sequence. Show your work. Hint: A.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Considera series of diagonal squares, constructed as shown below:
中
OR=1
n=2
n= 4
Note that the "3 x 3" square has area 13, and the 4 x 4 square has area 25. Our goal is the find a
formula for the area of an nx n" (diagonal) square.
(a) Write out the first six terms of the sequence of areas (assume a = 1, ag = 5, etc).
(b) Use your results from part (a) to find a closed formula for the sequence. Show your work. Hint: A.
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