Please explain the first statement and solve it explicitly. thank you
The sum of k consecutive and positive integers in a sequence is S. If k is between 1 and 100, inclusive, what is the probability that \frac{S}{k} results in a value that is part of the sequence?
k = no. of integers in the series
s = sum of the numbers in series
s/k, therefore, is the average of the series
if k is an odd number for eg 3, the numbers would be:
n, n+1, n+2
s = 3n + 3
s/k = n + 1 , ie the 2nd term
You will find that for all odd numbers, the mean would be the middle number
For even k, for eg 4, the numbers would be:
n, n+1, n+2, n+3
s = 4n + 6
s/k = n + 1.5 , not a term
The probability terefore will be 0.5
is this correct ?
since it is consecutive numbers. s/k is average, avg should lie in the series.
ie case 1: 1 to 5, avg is (1+5)/2=3 .
case 2: 1 to 4 , avg will be 2.5 so , if series is even length ,s/k wont be there, so its a 50/50
and answer was .5
@Leaderboard
Looks reasonable to me.
