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

Let the function such that
f(x-1)+f(x+1)=31/2f(x), x€R.If f(5)=100, find ∑99r=0(5+12r).

 

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 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
askIITians Faculty

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