Why Ramanujan summation is actually -3/32

Few weeks ago my roommate effusively started telling me that the sum of all natural numbers is –1/12, that is:

1+2+3+4+5+6+7+8 +… = –1/12

I was quite surprised with this statement, specially hearing it from an engineering graduate student.

I myself have a Math background. I studied infinite series back and forth at the beginning of my career, and know some possible leaks that can appear in a demonstration of series convergence. Hence, I already knew what the trick was here, and also I know for a fact that…