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  4. (1/4.5)+(1/5.6)+(1/6.7)+....+(1/(n+3)(n+4))

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Q. $\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{\left(n+3\right)\left(n+4\right)}$

Principle of Mathematical Induction

Solution:

Put n = 2. $S_2 = \frac{1}{4.5} + \frac{1}{5.6} = \frac{1}{12}$
option (2) = $\frac{2}{4(2+4)} = \frac{1}{12}$