Factorize completely ac - 2bc - a\(^2\) + 4b\(^2\)

Find the sum to infinity of the series 1/2 , 1/6, 1/18, .....

The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64 cm long, find the length of pendulum whose period is 9 sec

Three teachers shared a packet of chalk. The first teacher got 2/5 of the chalk and the second teacher received 2/15 of the remainder. What fraction did the third teacher receive?