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8 years, 8 months ago
8 years, 1 month ago
Hi,
We know that f(k) is the sum of the cubes of the numbers.
f(k)=[k(k+1)/2]^2 = 3^n
=> k^2 X (k+1)^2 = 3^n X 2^2
So, either k or k+1 has to be equal to 2. If k+1 = 2, k=1. in this case f(k) won't be a perfect power of 3.
If k=2, k+1 =3 and f(k) will be a perfect power of 3.
Thus, the answer to this question is B.