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

Let the function such that
f(x-1)+f(x+1)=31/2f(x), x€R.If f(5)=100, find
 r=099∑f(5+12r).

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1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago

Hello Student,
f(x-1)+f(x+1)=3^1/2f(x)
=>f(x)+f(x+2)=3^1/2f(x+1)
x to x+2
f(x+1)+f(x+3)=3^1/2f(x+2)
=>f(x-1)+2f(x+2)+f(x+3)=sqrt3(sqrt3(f(x+1)))
=>f(x-1)+f(x+3)=f(x+1)
x to x+2
f(x+1)+f(x+5)=f(x+3)
f(x-1)+f(x+5)=0
=>f(x)=-f(x+6)
=>f(x)=f(x+12)
=> period =12
=>sum =100*f(5)
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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