The math is less messy that way.........................working from powers of ten in numerators........but there is an odd number........of terms........from 1/11 to 1/100..........including........1/11 and 1/100.....would be 90 numbers...........so 45 pairs............b/c u have to cut the number of numbers in half....................1 - 100.....................101 * 50 = 5050..........how Gauss did it........he just added beg to end....................and multiplied by number of pairs.........there are 100 numbers.....from 1 to 100......including 1 and 100..........................but if u took 1/10 to 1/100.........there are 91 terms............a fraction number of pairs................so from 1/11 to 1/100.........there are 45 pairs...........of a messing number...............the 3rd below..................MS Excel.....says the estimated sum is 4.5..............of course that is one number less.........on average................but it does not work out exactly....................the way Gauss did it.........it cannot work out exactly......the dec values do not go down uniformly..........so it is an estimate.................not an exact amount...............interesting 91...........from 10 to 100..............................including 10 and 100 in the denominator.............that matches....................91 - 19 = 72........with 71 integers...............a kind of garbled e..................1/9 and 1/10..............becoming.....19 and 110...................the difference being 91............19 also........the last double digit prime..............................of the 1st 4 primes in double digits...........like 14i........1st 4.........a 1 and a 4.............those four........gives the clue to the end digit.................there might be a way to figure the value of the hs......without adding term by term......................................I do not know analysis............................I do not even know why the zeroes tell u everything imp.................I take their word for it.................................I barely even know calculus........

0.0909091

0.01

0.10090909090909100

45.00

4.540909091