Question

Prove that the sum of all natural numbers is -1/12.

Answer 1

This is not true. The infinite series



`\displaystyle\sum_(n=1)^\infty n`

converges if and only if the sequence of its partial sums converges. The
`k`-th partial sum is


`\displaystyle\sum_(n=1)^kn=\frac{k(k+1)}2`

but clearly this diverges as
`k` gets arbitrarily large.