AP EAMCET · Maths · Sequences and Series
The sum of the cubes of three consecutive natural numbers is divisible by
- A 26
- B 25
- C 9
- D 7
Answer & Solution
Correct Answer
(C) 9
Step-by-step Solution
Detailed explanation
Let the three consecutive natural numbers \((n-1), n, n+1\) where \(n \geq 2\) \(\therefore\) Sum of cubes of the three consecutive natural numbers is \((n-1)^3+n^3+(n+1)^3=3 n^3+6 n=3 n\left(n^2+2\right)\) For each value of \(n \geq 2\), the expression \(3 n\left(n^2+2\right)\)…
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