A function satisfies f(x-y)= f(x) f(y) , where f(y) 0 . If f(1)=0.5 , then what is f(2)+f(3)+f(4)+f(5)+f(6) equal to?

Step-by-step solution

aligned & Since, f (2-1)= f (1)= f (2) f (1) & f (2)=( f (1))^2= 5 10 5 10 = 1 4 & f (3-2)= f (1)= f (3) f (2) 1 2 = f (3) 1 4 f (3)= 1 8 & Similarly we get f (4)= 1 16 , f (5)= 1 32 , f (6)= 1 64 & Now, f (2)+ f (3)+ f (4)+ f (5)+ f (6) & = 1 4 + 1 8 + 1 16 + 1 32 + 1 64 = 31 64 aligned