16. Its coming out to be D

(1 - q^128)/1-q

as when you multiply the denominator and numerator by (1-q)

(1-q)(1+q)=(1-q^2)

(1-q^2)(1+q^2) = (1-q^4)

...

and it becomes

(1-q^64)(1+q^64) = (1-q^128)

51. 15 days

52. student studied d(morning and evening) days. Thus total of 2d mornings + afternoons

(d days -> d mornings + d afternoons)

and it rained for 7 days ( evenings or mornings.) with 5 clear afternoons and 6 clear afternoons

so eqn becomes

7 + 5 + 6 = 2d

or d=9 days

"Woh mara papad wale ko!"