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Differential Calculus> Let the function such that f(x-1)+f(x+1)=...

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Let the function such that
f(x-1)+f(x+1)=3^1/2f(x), x€R.If f(5)=100, find ∑⁹⁹_r=0(5+12r).

vineet nimesh , 10 Years ago

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1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:

$f(x-1)+f(x+1) = \sqrt{3}f(x)$

$f(5) = 100$

$S = \sum_{r=0}^{99}5 + 12r$

$S = (5\times 99) + 12\sum_{r=0}^{99}r$

$S = (5\times 99) + (12\times \frac{99(100)}{2})$

$S = 99(5+600)$

$S = 99\times 605$

$S = 59895$

Thanks & Regards

Jitender Singh

IIT Delhi

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