COMEDK · Maths · 5. Sequences and Series
If the sum of first \(n\) natural numbers is \(\frac{1}{78}\) times the sum their cubes, then the value of \(n\) is
- A 11
- B 12
- C 13
- D 14
Answer & Solution
Correct Answer
(B) 12
Step-by-step Solution
Detailed explanation
Since, \(\Sigma n=\frac{1}{78} \Sigma n^{3}\) \[ \begin{array}{ll} \Rightarrow & \frac{n(n+1)}{2}=\frac{1}{78} \times \frac{n^{2}(n+1)^{2}}{4} \\ \Rightarrow & n^{2}+n-156=0 \\ \Rightarrow & (n+13)(n-12)=0 \\ \Rightarrow & n=12 \quad \quad[n \neq-13] \end{array} \]
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