`A = 1 + 2 + 3 + .... + 100`
`A = ( 100 +1 ) . 100 : 2`
`A = 101 . 100 : 2`
`A = 10100 : 2`
`A = 5050`
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`B = 1/(1 . 2 ) + 1/( 2 . 3 ) + .... + 1/( 99 . 100 )`
`B = 1/1 - 1/2 + 1/2 - 1/3 + .... + 1/99 - 1/100`
`B = 1 - 1/100`
`B = 99/100`
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`C = ( 1 - 1/2 ) . ( 1 - 1/3 ) . ( 1 - 1/4 ) .... ( 1 - 1/100 )`
`C = 1/2 . 2/3 . 3/4 .... 99/100`
`C = ( 1 . 2 . 3 .... 99 )/( 2 . 3 . 4 .... 100 )`
`C = 1/100`
`⇒ A . B . C = 5050 . 99/100 . 1/100 = 9999/4`
