# 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!

**{ (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**

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

** ****è****lim (2n ^{2}+1) /n^{2}) = lim (2 +1/n^{2}) =2/4=1/2**

** (4n ^{2}-3n /n^{2}) (4-3/n) **

**è****(if n****à****∞,then 1/n or 1/n ^{2} **

**à**

**0, hence**

**è**

**1/2)**

**Since limit is a finite number (****è****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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