Sequences and Series

If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in A.P., prove that a, b, c are in A.P.

Find the sum of the following series up to n terms:

(1³ / 1) + ((1³ + 2³) / (1 + 3)) + ((1³ + 2³ + 3³) / (1 + 3 + 5)) + …