Mathematicians have just created three new operation symbols, @, $,and _, each doing a different thing to a pair of numbers (All of these symbols can be derived from already-known operations and notations). The following equations using the new symbols are correct:
5@5= 2/5
2@2= 1
2@3= 5/9
3@4= 7/16
2@4= 3/8
1$0= undefined
1$4= 1/10
4$1= 1/10
10$10= 1/50
(1@1) $ 1= (√2)/10
2_2= 6
2_3= 9
6_2= 42
3_5= 30
5_6= 90
If the previous equations are correct, compute the following equation.
1 @ (1 $ (1_1))=
2_2= 6
2_3= 9
6_2= 42
3_5= 30
5_6= 90
6/2= 3 = 2+1
9/3= 3 = 2+1
42/2= 21 = 6+5+4+3+2+1
30/5= 6 = 3+2+1
90/6= 15 = 5+4+3+2+1
a_b = b*a*(a+1)/2
The _ operator
