AP EAMCET2005MathematicsBasics of Mathematics
If N denotes the set of all positive integers and if f: N N is defined by f(n)= the sum of positive divisors of n then, f (2^k 3 ) , where k is a positive integers, is
Options
- A2^ k+1 -1
- B2 (2^ k+1 -1 )
- C3 (2^ k+1 -1 )
- D4 (2^ k+1 -1 )
Correct answer
C. 3 (2^ k+1 -1 )
Step-by-step solution
Given that f(x)= the sum of positive divisors of n . aligned f (2^k 3 ) & =3 (1+2+2^2+2^3+ +2^k ) & =3 (2^ -k+1 -1 ) 2-1 =3 (2^ -k+1 -1 ) aligned