Euler constant: 0.57721566490153286060651209008240243104


http://mathworld.wolfram.com/HarmonicNumber.html


Euler-Mac-Laurin:
n=1000000; print(log(n)+Euler+1/(2*n)); print(log(n)+Euler+1/(2*n)-1/(12*n^2));
           print(log(n)+Euler+1/(2*n)-1/(12*n^2)+1/(120*n^4));
	   print(log(n)+Euler+1/(2*n)-1/(12*n^2)+1/(120*n^4)-1/(252*n^6));

    	       14.39272672286580696471446081818858767
    	       14.39272672286572363138112748485525434
    	       14.39272672286572363138112749318858768
    	       14.39272672286572363138112749318858768

n=10000000
    	       16.69531136585985264873245227287295188
    	       16.69531136585985181539911893953961855
    	       16.69531136585985181539911893954045188
    	       16.69531136585985181539911893954045188

n=100000000
    	       18.99789641385389833275044372755731609
    	       18.99789641385389832441711039422398276
    	       18.99789641385389832441711039422398284
    	       18.99789641385389832441711039422398284


H(1000000)    = 14.392726722865723631381127493188587676644800013744311653418433045812958507517995
H(10000000)   = 16.695311365859851815399118939540451884249869752373080462785135954356288692174254
H(100000000)  = 18.997896413853898324417110394223982841850971244970103438818422188657611302609182
H(1000000000) = 21.300481502347944016685101848908346966127072733598880383101750089624767245624035