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What is Convergence and Divergence in Calculus Mathematics ?

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 it’s limit value does not exist(or rather approaches infinity).

Convergence and Divergence in sequences:

arrow   Convergence and Divergence

Convergence and Divergence 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

  -> To find the limit, divide the numerator and denominator with the highest exponent.

Convergence and Divergence

->         (if n -> ∞,then 1/n or 1/n2 à0, hence -> 1/2)

Since limit is a finite number( -> 1/2), hence the Sequence Converges!

Convergence and Divergence of Series:

Convergence and Divergence

Example:

Determine if Series converges or diverges.

 ∑n(n+1)/2

                                                  -> lim n(n+1)/2 = ∞, hence the Series Diverges.

 

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You can also Read our other blog How Do Find That Equation Is A Linear Or Nonlinear Function?

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