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αn = 2^n + 3 · 5^n / 4^n + 5^n  where  n = 1, 2, . . . . Show that {αn} con

αn = 2^n + 3 · 5^n / 4^n + 5^n  where  n = 1, 2, . . . . Show that {αn} con

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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Let
αn = 2^n + 3 · 5^n / 4^n + 5^n  where  n = 1, 2, . . . .
Show that {αn} converges to 3 with the rate of convergence O(( 4/5)^n).

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