Convergence and Divergence
In Sequences and Series, we can find whether the given function converges or diverges. A function is said to converge if its limit value exists and is finite. A function is said to diverge if its limit value does not exist (or rather approaches infinity).
Convergence and Divergence in sequences:
Example:
Determine if sequence converges or diverges!
{ (2n2+1)/(4n2-3n) }∞n=1
In order to find whether the sequence converges or diverges, take the limit of the given function
è To find the limit, divide the numerator and denominator with the highest exponent.
èlim (2n2+1) /n2) = lim (2 +1/n2) =2/4=1/2
(4n2-3n /n2) (4-3/n)
è(if nà∞,then 1/n or 1/n2 à0, henceè1/2)
Since limit is a finite number (è1/2), hence the Sequence Converges!
Convergence and Divergence of Series:
Example:
Determine if Series converges or diverges.
∑n(n+1)/2
lim n(n+1)/2 = ∞, hence the Series Diverges.
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