Definition:
A sequence (an) is convergence to a number l. If given excellon >0 there exist a positive integer m. Such that mod an - l < excellon for all n>=m. l is the limit of the sequence. And lim n->∞ an=l (or) (an) -> l.
Note:
(an) -> l if and only if given excellon>0 there exist a natural number m. Such that mod an-l< for all n>=m, All but a finite number of terms of the sequence le with in the interval (l-excellon, l+excellon).
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SIMPLE HARMONIC MOTION
INTRO
A very common and important type of motion occurring in nature is that which involves osci- Important Basic Theorem
Statement:
Let (an) be any sequence. And lim n -> infinity (an/an+1) = l if l > 1 th
- Show that if (an) ->0 and (bn) is bounded, then (anbn) ->0
Since (bn) is bounded, there exist k >0 such that mod bn <=k for all n.
Therefore, mod anbn
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From a Wild Child To a Virtuous HeroONE MAN UNITED HIS COUNTRYFrom EMMY NOMINATED DIRECT