Question:

A function f(x) is defined as f(x) = f(x – 2) + x(x – 2) for all the integer values of ‘x’. Given that f(1) + f(6) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?

Answer:

Method:

f(x) = f(x – 2) + x(x – 2)

f(1) + f(6) = 0 => f(6) = -f(1)

f(2) = f(0)

f(3) = f(1) + 3

f(4) = f(2) + 8

f(5) = f(1) + 18

f(6) = f(4) + 24 = f(2) + 32

f(2) = -f1 - 32

f(4) = -f1 -24

f(1) + ... f(6) = -f1 -32 -f1 - 24 + f1 + 3 + f1 + 18

= -56 + 21 = -35.