Answer:
Step-by-step explanation:
the 1st number of this series is x
because this series has 384 consecutive odd integers => this is a arithmetic sequence with d = 2
=> the sum of this series = [tex]384x+384(384-1) =384x+147072[/tex]
but this series has a sum that is the perfect fourth power of a positive integer
=> 384x + 147072 = k^4 ( k is a positive integer)
to have the smallest sum => x must be the smallest odd integer.
+) with the sum = 104 976 => x isnt a integer => unreasonable
+) with the sum = 20 736 => x = -329
+) with the sum = 10000 =>x isnt a integer => unreasonable
+) with the sum = 1296 => x isnt a integer => unreasonable
+) with the sum = 38 416 => x isnt a integer => unreasonable
=> the smallest sum is 20 736
