a) A = 4/5.9 + 4/9.13 + 4/13.17 + ... + 4/41/45
A = 1/5 - 1/9 + 1/9 - 1/13 + 1/13 - 1/17 + ... + 1/41 - 1/45
A = 1/5 - 1/45
A = 8/45
b) B = ( 1 - 1/2 ) . ( 1 - 1/3 ) . ( 1 - 1/4 ) . ..... . ( 1 - 1/100 )
B = 1/2 . 2/3 . 3/4 . .... . 99/100
B = \(\frac{1.2.3.......99}{2.3.4......100}\)
B = 1/100
B = \(\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{3}\right)+...+\left(1-\frac{1}{100}\right)\)
B = \(\frac{1}{2}.\frac{2}{3}.....\frac{99}{100}\)
B = \(\frac{1}{100}\)