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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.
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