How to solve 2+2=5 without flaws?

We have A=1+2+3+4+5+...

=1+(2+3+4)+(5+6+7)+(8+9+10)+...

=1+9(1)+9(2)+9(3)+...

=1+9(1+2+3+...)

Replace 1+2+3+...=A we have A=1+9A<=>A=-1/8

Again we have A=1+2+3+...

=1+2+(3+4+5)+(6+7+8)+(9+10+11)+...

=3+12(1)+12(2)+12(3)+...

=3+12(1+2+3+...)

Replace again we have A=3+12A<=>A=-3/11

Remember -1/8 a value of A? So -1/8=-3/11

<=>11=24

<=>0=13

<=>0=1(both divided 13)

<=>2+2=2+2+1

<=>2+2=5

(perfect -_-)