16 Use Theorems 9.9 and 9.10 or Exercises 9.9-9.15 to prove the following: (a) lim nª+8n n² +9 (b) lim[+(-1)"] = +∞ (c) lim[32 321=+m = +∞
16 Use Theorems 9.9 and 9.10 or Exercises 9.9-9.15 to prove the following: (a) lim nª+8n n² +9 (b) lim[+(-1)"] = +∞ (c) lim[32 321=+m = +∞
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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THEOREM 9.10 For a sequence (sn) of positive real numbers, we have lim sn = +∞ if and only if lim(1/sn ) = 0.
THEOREM 9.9
Let (sn) and (tn) be sequences such that lim sn = +∞ and lim tn > 0 [lim tn can be finite or +∞]. Then lim sntn = +∞.
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