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Q.
The series of differences between consecutive prime numbers is represented as Cp1, Cp2, Cp3, .... Cpn , Whare Cp1 is the difference between the second and the first prime number. Find the sum of series when n = 23, given that the 23rd prime number is 83 ?
A.
87
B.
81
C.
83
D.
85
View Answer
Correct choice: A
Explanation:
Cp1 = p2 - p1 , Cp2 = p3 - p2 .. .. .. Cp23 = p24 - p23 Sum of series = (p2-p1) + (p3-p2) + .....(p23-p22) + (p24-p23) All terms get cancelled, except p1 = 2 and p24 = 89 So Sum = -p1 + p24 Sum of series = -2 + 89 = 87
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