This argument is similar to the one $$ \sum_{n=1}^\infty n = -1/12 $$ which went viral a few years ago. You are actually using methods which were originally designed for manipulating absolutly convergent series on series which are not convergent at all. There has much talk been done and I think our friends of numberphile can explain it the best:

• Introduction
• Clarification
• How to asign numbers to none-convergent series

This argument is similar to the one $$ \sum_{n=1}^\infty n = -1/12 $$ which went viral a few years ago. You are actually using methods which were originally designed for manipulating absolutly convergent series on series which are not convergent at all. There has much talk been done and I think our friends of numberphile can explain it the best:

• Introduction
• Clarification
• How to assign numbers to none-convergent series