Answer is 51
Explanation:
By mathematical induction,solve this from smaller value to bigger value
fun(1) → fun(2) → fun(3) → fun(4) → fun(5)
For n=1,it check if(1=1).The condition is true so it return 1;
For n=2,The if condition fails then it execute for loop for k<2 times
For k=1,
x=1+fun(1)*fun(2-1); => 1+fun(1)*fun(1) => 1+1*1 => 2
it returns x=2 so fun(2)=2
For n=3,The if condition fails then it execute for loop for k=1,2
For k=1,
x=1+fun(1)*fun(3-1); => 1+fun(1)*fun(2) => 1+1*2 => 3
For k=2,
x=3+fun(2)*fun(3-2); => 3+fun(2)*fun(1) => 3+2*1 => 5
It return x =5 => fun(3)=5
For n=4,The if condition fails then it execute for loop for k=1,2,3
For k=1,
x=1+fun(1)*fun(4-1); => 1+fun(1)*fun(3) => 1+1*5 => 6
For k=2,
x=6+fun(2)*fun(4-2); => 6+fun(2)*fun(2) => 6+2*2 => 10
For k=3,
x=10+fun(3)*fun(4-3); => 10+fun(3)*fun(1) => 10+5*1 => 15
It return x =15 => fun(4)=15
For n=5,The if condition fails then it execute for loop for k=1,2,3,4
For k=1,
x=1+fun(1)*fun(5-1); => 1+fun(1)*fun(4) => 1+1*15 => 16
For k=2,
x=16+fun(2)*fun(5-2); => 16+fun(2)*fun(3) => 16+2*5 => 26
For k=3,
x=26+fun(3)*fun(5-3); => 26+fun(3)*fun(2) => 26+5*2 => 36
For k=4,
x=36+fun(4)*fun(5-4); => 36+fun(4)*fun(1) => 36+15*1 => 51
It return x =51 => fun(5)=51.