1+2+3+4+5+.....= -0.083333.. This is the sum of Riemann's zeta function at s=-1
1^3+2^3+3^3+4^3+.....=ζ(3) = 1.20205690315959428539973..........etc.
This is called "Aprey's constant", which is the sum of Riemann's zeta function at s=3
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+9665 The first line is contradictory. How can a bunch of positive integers add up and became a negative fraction which is \(-\dfrac{1}{12}\)?
But I will solve this.
\(1+2+... = -\dfrac{1}{12}\\ 1^3+2^3+...... = (1+2+.... )^2=(-\dfrac{1}{12})^2=\dfrac{1}{144}\)
This is still contradictory because the sum of a bunch of third powers of a negative number is a positive number.
