If the set of natural numbers is closed under addition, how can we have the result that the sum of all the natural numbers to infinity is -1/12
4340
Why does $1+2+3+\cdots = -\frac{1}{12}$?
106028
Sum of $\frac{1}{(2n)(2n+1)}$ from $1$ to infinity
98082
Another combinatorics problem: $\sum\limits_{k = 0}^n (-1)^k \binom{2n-k}k2^{2n-2k}=2n+1$
36694
Sum of first n natural numbers proof
132264
Is there a (basic) way to understand why a limit cannot be brought inside of a sum, in certain situations?
28683
Sum of two closed sets in $\mathbb R$ is closed?
49982
Closed expression for infinite series
37783
Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
108748
Why there are real numbers with infinite digits, but no such natural numbers (or another reason why real numbers are uncountable)
119606
Closed form of summation
69084
What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?
55777
A tricky sum to infinity
55061
Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
141978
How to find the infinite sum
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
75995
Infinite Sum - Result not correct for all cases?
48051
Proof related to natural numbers