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Question: given g(0)=1,g(1)=-1and g(n)=g(n-1)+g(n-2),find(6).
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| October 10, 2007 01:56:58 |
#1 |
| santosh |
Member Since: Visitor Total Comments: N/A |
RE: given g(0)=1,g(1)=-1and g(n)=g(n-1)+g(n-2),find(6)...
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# substitute n=6
=> g(6) = g(5)+g(4)----------------(1)
# sub n=5
=> g(5) = g(4)+g(3)-----------------(2)
# sub n=4
=> g(4) = g(3)+g(2)------------------(3)
#sub n=3
=> g(3)= g(2)+g(1)--------------------(4)
# sub n=2
=> g(2)= g(1)+g(0)--------------------(5)
so ,
g(2) = 0;
g(3)= -1;
g(4) = -1;
g(5)= -2;
g(6) = -3;
another method:
g(6) = 5*g(1)+g(0)
so generalised solution is g(a) = (a-1)*g(1) + g(o) where a is to find for the given equation g(n) = g(n-1)+g(n-2) |
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