csat-suneung 2005 Q30 (Discrete Mathematics)

csat-suneung · South-Korea · csat__math-science 4 marks Sequences and Series Evaluation of a Finite or Infinite Sum
For a natural number $k$, when $n = 5 ^ { k }$, $f ( n )$ satisfies $$f ( 5 n ) = f ( n ) + 3 , \quad f ( 5 ) = 4$$ Find the value of $\sum _ { k = 1 } ^ { 10 } f \left( 5 ^ { k } \right)$. [4 points]
For a natural number $k$, when $n = 5 ^ { k }$, $f ( n )$ satisfies
$$f ( 5 n ) = f ( n ) + 3 , \quad f ( 5 ) = 4$$
Find the value of $\sum _ { k = 1 } ^ { 10 } f \left( 5 ^ { k } \right)$. [4 points]