**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:**

**Convergence and Divergence Example: **Determine if sequence converges or diverges!

** { (2n ^{2}+1)/(4n^{2}-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.

**-> ** **(if n -> ****∞,then 1/n or 1/n ^{2} **

**à**

**0, hence ->**

**1/2)**

**Since limit is a finite number( -> ****1/2), 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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