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Revision difference : harmonic series
Version 3 - Version 2
1c1 < xxxxxxxx --- > yyyyyyyy 13c13 < Here, each parenthetic sum contains a number of terms twice as many as the preceding one.\, The sum in the first pair of parentheses is graater than\, $2\cdot\frac{1}{4} = \frac{1}{2}$,\, the sum in the second pair of parentheses is greater than\, $4\cdot\frac{1}{8} = \frac{1}{2}$;\, thus one sees that the sum in all pairs of parentheses is greater than $\frac{1}{2}$.\, Consequently, the partial sum of $n$ first terms exceeds any given real number, when $n$ is sufficiently big.\\ --- > Here, each parenthetic sum contains a number of terms twice as many as the preceding one.\, The sum in the first parentheses is greater than\, $2\cdot\frac{1}{4} = \frac{1}{2}$,\, the sum in the second parentheses is greater than\, $4\cdot\frac{1}{8} = \frac{1}{2}$;\, thus one sees that the sum in all parentheses is greater than $\frac{1}{2}$.\, Consequently, the partial sum of $n$ first terms exceeds any given real number, when $n$ is sufficiently big.\\
