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The function defined for positive integers by $F(1)=1,F(2)=1,F(3)=-1$ and by identities F(2k)=F(k),F(2k+1)=F(k) for $ k>=2.$The sum $F(1)+F(2)+F(3)+...+F(100)$ is________

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Let's start series by ignoring first 3 numbers. So F(4)=1,F(5)=1,F(6)=-1,F(7)=-1,F(8)=1,F(9)=1,F(10)=1,F(11)=1,

We observe that +1 and -1 will occur simultaneously as +2,-2,+4,-4,+8,-8,+16,-16,+32 .Now total terms are 92.So,until 97 5 times -1 will be there so,32 -5=27, Now adding +1 as F(0)+F(1)+F(2)=1 So,27+1=28

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