By the principle of mathematical induction prove that the following statements are true for all natural numbers 'n'
`(a) (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+......+(1)/((2n-1)(2n+1)) =(n)/(2n+1)`
`(b) (1)/(1.4)+(1)/(4.7)+(1)/(7.10)+......+(1)/((3n-2)(3n+1))` `=(n)/(3n+1)`
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Explanation

To prove the given statements using the principle of mathematical induction, we will follow these steps for both parts (a) and (b).

### Part (a)

**Statement to Prove:**
\[ \frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \ldots + \frac{1}{(2n-1)(2n+1)} = \frac{n}{2n+1} \]
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