JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(f(x)\) be a function such that \(f(x+y)=f(x) \cdot f(y)\) for all \(x , y \in N\). If \(f (1)=3\) and \(\sum \limits_{ k =1}^{ n } f ( k )=3279\), then the value of \(n\) is \(.........\)
- A \(6\)
- B \(8\)
- C \(7\)
- D \(9\)
Answer & Solution
Correct Answer
(C) \(7\)
Step-by-step Solution
Detailed explanation
\(f ( x + y )= f ( x ) \cdot f ( y ) \forall x , y \in N , f (1)=3\) \(f (2)= f ^2(1)=3^2\) \(f (3)= f (1) f (2)=3^3\) \(f (4)=3^4\) \(f ( k )=3^{ k }\) \(\sum_{ k =1}^{ n } f ( k )=3279\) \(f (1)+ f (2)+ f (3)+\ldots \ldots \ldots+ f ( k )=3279\)…
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