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Problem 10.1.10. (a) Use the fact that for large n, 1+1/2+3+... + ≈ ln (n + 1) + y to determine approximately how large n must be to make 1 1 1 1+ + + + > 100. 2 3 n (b) Suppose we have a supercomputer which can add 10 trillion terms of the Harmonic Series per second. Approximately how many earth lifetimes would it take for this computer to sum the Harmonic Series until it surpasses 100?

Problem 10.1.10. (a) Use the fact that for large n, 1+1/2+3+... + ≈ ln (n + 1) + y to determine approximately how large n must be to make 1 1 1 1+ + + + > 100. 2 3 n (b) Suppose we have a supercomputer which can add 10 trillion terms of the Harmonic Series per second. Approximately how many earth lifetimes would it take for this computer to sum the Harmonic Series until it surpasses 100?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 10.1.10. n (a) Use the fact that for large n, 1+ 2+ 3+ + ½⁄2 ≈ ln (n + 1) + y to determine approximately how large n must be to make 1 1 1 1+ + + + >100. 2 3 n (b) Suppose we have a supercomputer which can add 10 trillion terms of the Harmonic Series per second. Approximately how many earth lifetimes would it take for this computer to sum the Harmonic Series until it surpasses 100?
Transcribed Image Text:Problem 10.1.10. n (a) Use the fact that for large n, 1+ 2+ 3+ + ½⁄2 ≈ ln (n + 1) + y to determine approximately how large n must be to make 1 1 1 1+ + + + >100. 2 3 n (b) Suppose we have a supercomputer which can add 10 trillion terms of the Harmonic Series per second. Approximately how many earth lifetimes would it take for this computer to sum the Harmonic Series until it surpasses 100?
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