Let f:W –W be a given function satisfying f(x)=f(x-1)+f(x-2) for x>2 or x=2. If f(0)=0 and f(1)=1, then find the value of f(2)+f(3)+f(4)+f(5)+f(6).

Asked by Anil | 11th May, 2017, 12:21: PM

Expert Answer:

begin mathsize 16px style straight f left parenthesis straight x right parenthesis equals straight f left parenthesis straight x minus 1 right parenthesis plus straight f left parenthesis straight x minus 2 right parenthesis space for space straight x greater or equal than 2 space
straight f left parenthesis 2 right parenthesis equals straight f left parenthesis 1 right parenthesis plus straight f left parenthesis 0 right parenthesis equals 1 plus 0 equals 1
straight f left parenthesis 3 right parenthesis equals straight f left parenthesis 2 right parenthesis plus straight f left parenthesis 1 right parenthesis equals 1 plus 1 equals 2
straight f left parenthesis 4 right parenthesis equals straight f left parenthesis 3 right parenthesis plus straight f left parenthesis 2 right parenthesis equals 2 plus 1 equals 3
straight f left parenthesis 5 right parenthesis equals straight f left parenthesis 4 right parenthesis plus straight f left parenthesis 3 right parenthesis equals 3 plus 2 equals 5
straight f left parenthesis 6 right parenthesis equals straight f left parenthesis 5 right parenthesis plus straight f left parenthesis 4 right parenthesis equals 5 plus 3 equals 8
rightwards double arrow straight f left parenthesis 2 right parenthesis plus straight f left parenthesis 3 right parenthesis plus straight f left parenthesis 4 right parenthesis plus straight f left parenthesis 5 right parenthesis plus straight f left parenthesis 6 right parenthesis equals 19 end style

Answered by Sneha shidid | 11th May, 2017, 04:30: PM