text: what is the value of this serie [1+1/2+1/3+1/4+...........+1/n]?   answer: infinity  explanation: use the logarithmic expansion series log(1-x)  = - x - x^2/2 - x^3/3 - x^4/4 ..... - x^n/n - .... to infinity  putting x = 1 the equation becomes log(1-1) = - (1 + 1/2 + 1/3 + 1/4 +... + 1/n +... to infinity) or log(0) = - (given series) or - log(0) = given series or log(1/0) = given series i.e. given series = log(infinity) = infinite.  additional comments: test for convergence of the series and you will find that the series is divergent (try 'mu'-test or comparison test).