Telescopic sum
Posted: Sat Jan 16, 2016 11:49 pm
Evaluate the sum:
$$\mathcal{S}= \frac{1}{\sin \left ( 45 ^0\right )\sin \left ( 46^0 \right )}+\frac{1}{\sin \left ( 47^0 \right )\left ( \sin 48^0 \right )}+\cdots+\frac{1}{\sin \left ( 133^0 \right )\sin \left ( 134^0 \right )}$$
$$\mathcal{S}= \frac{1}{\sin \left ( 45 ^0\right )\sin \left ( 46^0 \right )}+\frac{1}{\sin \left ( 47^0 \right )\left ( \sin 48^0 \right )}+\cdots+\frac{1}{\sin \left ( 133^0 \right )\sin \left ( 134^0 \right )}$$