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Unformatted text preview: ms must have a limit of 0. Example
n 1 n
n n 1 lim an is convergent. a is divergent. n Example
n n lim an a n is convergent.
Not necessarily convergent. Stay tuned for the answer. Divergence Test an
lim an 0
If , then the series, , is divergent.
n n 1 (This test is a consequence of the theorem.) Limit Laws
If and are convergent, and and
a b b b , then , , and are can a b convergent, and
n n n n n i) ca ca
ii) a b a b
iii) b a b
a n n n n n n n n Summary
an lim an L
If , and L is finite, then is convergent.
n lim an 0
If ,then is divergent. an
n A geometric series is convergent if the magnitude of the common ratio is less than 1.
1 r If a geometric series is convergent, the sum is , where r is the common ratio and a is the first term....
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This note was uploaded on 02/24/2014 for the course APMA 1110 taught by Professor Morris during the Fall '11 term at UVA.
- Fall '11