Question

# 1+2+3+4+..... Infinity=? Are in A.P.

Solution

## Obviously, it is -1/12. That's definitely the only answer that makes sense (sarcasm intended). To see why, we should prove it in three parts. First, consider the series K = 1-1+1-1+1-1.... K+K = 1, so K = 1/2 Second, consider the series J = 1-2+3-4+5-6.... J+J = K, so J = 1/4 Third, consider S = 1+2+3+4+5+6.... S-4S = 1-2+3-4+5-6... = J so S = -J/3 = -1/12

Suggest corrections