1+1/2+1/3+1/4+.......................upto hundred terms

Question

how to find the sum of an harmonic progression.is there a general formula for it.

Answer 1

me dont no av NE formula

If yuno how tu program, yu kood make a loop tu add it up

1+(1/2)=1.5

+(1/3)...0.333333giv 1.83333333333333...

+(1/4)...+0.25 giv 2.08333333333...

+(1/5)...+.2 giv 2.283333333333...

+(1/6)...+0.1666666666 giv 2.45

+1/7...+0.14285714285714  giv 2.59285714285714...

+1/8...+0.125 giv 2.71785714285714

+1/9...+0.11111111111111111111... giv 2.82896825396825

+1/10...+0.1   giv 2.92896825396825

+1/11...+0.09090909090909  giv 3.01987734487734

+1/12...+0.0833333333333   giv 3.10321067821067

+1/13...+0.07692307692308...giv  3.18013337503

+1/14...0.07142857142857...3.2515623265623197

1/15...0.06666666666666...3.31822899322899

1/16...0.0625...3.38072899322899

1/17...0.05882352941176...3.43955252264075

1/18...0.055555555555555...3.49510807819631

1/19...0.05263157894747...3.54773965714368

1/20...0.05...3.5977396571436797

Answer 2

The series doesn't converge, surprisingly enough, because you'd think so, since the terms are getting smaller. One way of looking at the series is to consider it as the sum of a set of geometric series that individually do converge: 1+1/2+1/4+1/8+... +1/3+1/9+1/27+... +1/5+1/25+1/125+... + 1/2(1/3+1/9+1/27+...) + 1/7+1/49+1/243+... + 1/2(1/5+1/25+...) +... , but that gets a bit hairy, too. Sum of first 100 terms=4.85404418431... according to my calculator and sleight of hand! I don't know of any formula, sorry. Best use a computer since it's a simple enough program:

a=0; x=0

While a<100 Do

a=a+1

x=x+1/a

Loop

Print x