Halp

The sum of the first 10 terms is given by:

S₁₀  = a [ 1 - r ⁿ ] / [ 1 - r ]     where a is the first term (48) , r is the common ratio (1/2) and n = 10

So we have :

S₁₀  = 48 [ 1 - (1/2)¹⁰] / [ 1 - 1/2]  =  3069/32  = 95.90625

The infinite sum =

a / ( 1 - r)  =  48 / [ 1/2]  = 48 * 2   = 96