[administration]

Q. The functions f(x) and g(x) are defined as: f(x) = f(x – 1) + x and g(x) = g(x – 1) + f(x), where x is an integer greater than or equal to 1. If f(0) = 0, then the value of k, for which g(k) – g(4) = g(10) – g(8), is

[administration]

g(k) = g(k-1)+f(k) = [g(k-2)+f(k-1)] +f(k)= [g(k-3)+f(k-2)]+f(k-1)+f(k) = [g(4)+f(5)] + f(6)+….+f(k)

 

so g(k)- g(4) = f(k)+ …+f(5);

g(10)-g(8) = f(10)+f(9)

f(1)=1, f(2)=2,

f(3)=6, f(4)=10,

f(5)=15, f(6)=21,

f(7)=28,f(8)=36,

f(9)=45, f(10)=55.

so g(10)-g(8) = 100,

 

now f(5)+f(6) +… f(k)= 100 so k =8.

[Author]

Posts