Intuition behind logarithm inequality: $1 - \\frac1x \\leq \\log x . . . The upper bound is very intuitive -- it's easy to derive from Taylor series as follows: $$ \log (1+x) = \sum_ {n=1}^\infty (-1)^ {n+1}\frac {x^n} {n} \leq (-1)^ {1+1}\frac {x^1} {1} = x $$ My question is: " what is the intuition behind the lower bound?
Is the sum of all natural numbers $-\frac {1} {12}$? [duplicate] So $$1+2+3+4+5+\dots $$ would be what we get as the limit of the partial sums $$1$$ $$1+2$$ $$1+2+3$$ and so on Now, it is clear that these partial sums grow without bound, so traditionally we say that the sum either doesn't exist or is infinite So, to make the claim in your question title, you must adopt a nontraditional method of summation