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Question

If $$f(n + 1) = f(n) + n$$ for all $$n \geq 0$$ or $$f(0) = 1$$, then $$f(200)$$ equals


A
21100
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B
21000
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C
20900
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D
19901
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Solution

The correct option is B $$19901$$
We have,
$$\begin{array}{l} f\left( { n+1 } \right) =f\left( n \right) +n \\ f\left( { 200 } \right) =\dfrac { n }{ 2 } \left( { a+l } \right) +1 \\ =\dfrac { { 199 } }{ 2 } \left( { 1+199 } \right) +1 \\ f\left( { 200 } \right) =19901 \end{array}$$

Hence, this is the answer.

Mathematics

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