Grade 12Differential Calculus
If f(1) =1, f(2n)= f(n), f(2n+1)=(f(n))^2 -2 for n=1,2,3,..., then find the value of f(1) + f(2) +...+f(25).
If f(1) =1, f(2n)= f(n), f(2n+1)=(f(n))^2 -2 for n=1,2,3,..., then find the value of f(1) + f(2) +...+f(25).
1 Answer
bindu
ans is 1..
put n=1 in f(2n)...then u get f(2)=f(1)=1....similarly put n=2,3....then u get
f(4)=f(6)=f(8)=......=f(24)=1..............(1)
now put n=1 in f(2n+1)=f(n)^2-2..........u get......f(3)=f(1)^2-2= (1-2) = -1
similarly..place n=2,3,...in that...u get f(5)=f(7)=f(9)=.....=f(25) = -1...........
now add them...u get 1
plz approve if ans is correct :)
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