Define the function f (x, y) = x + y + xy.

Natural numbers from 1 to 100 are written on the blackboard. A student comes and starts taking two numbers in order starting from the 1st pair as (1, 2), then the resultant of f (1, 2) = 1 + 2 + 1.2 = 5 with 3 will be calculated as f [f (1, 2), 3]
and, so on calculating the value of f (x, y).
What would be the final result at the end once all such values have been calculated?

(a) 100! – 1

(b) 101! – 1

(c) 101! + 1

(d) 100! + 1