Science:Math Exam Resources/Courses/MATH101/April 2018/Question 08 (ii)/Statement

Calculate

$$\displaystyle \sum _{n=2}^{\infty }\left({\frac {(-3)^{n}}{2^{2n}}}+{\frac {1}{\sqrt {n+2}}}-{\frac {1}{\sqrt {n+1}}}\right).$$