Paradox: Summation of natural logarithms Consider the expression : $$\sum_{i=1}^{\infty}\ln(i+2)-\ln(i+4)$$
If one evaluates it out, one gets $$\ln(\frac{3\times4\times5\times6\times...}{5\times6\times7\times8\times...})=\ln(12)$$  That value is positive.
However, each individual term of the original expression is negative, so the sum should be negative.
What's going on there?

$$\sum_{i=1}^{\infty} \ln(i+2)-\ln(i+4)$$
is a Telescoping serie in fact you can highlight the terms that cancel out by expanding the serie
$$\sum_{i=1}^{\infty} \ln(i+2)-\ln(i+4) = \ln(3)-\ln(5)+\ln(4)-\ln(6)+\ln(5)-\ln(7)+\ldots \\ = \ln(3)+\ln(4) - \infty = \ln(12) - \infty = -\infty$$
so actually there is not any paradox.
