Given F(n + 1) = (2F(n) + 1)/2, n ∈ N
⇒ F(n + 1) - F(n) = 1/2 .....(i)
Put n = 1, 2, 3, ..., 2014 in (i). we get,
F(2) – F(1) = 1/2
F(3) – F(2) = 1/2
F(4) – F(3) = 1/2 ... ... ... ... ... ...
F(2015) – F(2014) = 1/2
On addition, we get,
F(2015) – F(1) = 1/2 × 2014 = 1007
⇒ F(2015) = F(1) + 1007 = 1009
