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Let f : R → R be a function defined f x = 2 e 2 x e 2 x + e . Then f 1 100 + f 2 100 + f 3 100 + … + f 99 100 is equal to ______.

Correct answer

0

Step-by-step solution

f x = 2 e 2 x e 2 x + e f 1 − x = 2 e 2 1 − x e 2 1 − x + e = 2 e e + e 2 x Now, f x + f 1 − x = 2 i.e. f 1 100 + f 99 100 = 2 ⇒ f 1 100 + f 2 100 + ... f 99 100 = 2 × 49 + f 50 100 = 98 + 1 = 99

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