AP EAMCET · Maths · Functions
If \(1^4+2^4+3^4+\ldots+n^4=f(n)\) \(\left(1^2+2^2+\ldots+n^2\right), \forall n \in N\), then \(f(4)\) is equal to
- A \(\frac{58}{5}\)
- B \(\frac{57}{5}\)
- C \(\frac{59}{5}\)
- D \(\frac{56}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{59}{5}\)
Step-by-step Solution
Detailed explanation
We have, \(1^4+2^4+3^4+\ldots+n^4\) \(=f(n)\left(1^2+2^2+3^2+\ldots+n^2\right)\) \(f(n)=\frac{1^4+2^4+3^4+\ldots+n^4}{1^2+2^2+3^2+\ldots n^2}\) \(\Rightarrow f(4)=\frac{1^4+2^4+3^4+4^4}{1^2+2^2+3^2+4^2}\) \(=\frac{1+16+81+256}{1+4+9+16}\)…
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