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Question
If f( n + 1) = f (n) + n for all n ≥ 0 or f (0) = 1 then f (200) equals
If f( n + 1) = f (n) + n for all n ≥ 0 or f (0) = 1 then f (200) equals
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Solution
The correct option is D 19901
As f ( n + 1 ) = f (n) + n, we get f(n+1) - f(n) = n.
∴ Putting n = 0,1,2,.....199 in this equation successively and adding the two hundred resultant equations, we get after cancellations
f(200) - f(0) = 0+1+...+199 =
when f (0) = 1, f (200) = 19901.
19901
As f ( n + 1 ) = f (n) + n, we get f(n+1) - f(n) = n.
∴ Putting n = 0,1,2,.....199 in this equation successively and adding the two hundred resultant equations, we get after cancellations
f(200) - f(0) = 0+1+...+199 =
when f (0) = 1, f (200) = 19901.
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