If u did the same........from 1/11 to 1/100.....................................u can see..........that the fractions of the harmonic series...........do not go down uniformally.............so the estimate will NOT match the actual value.........................

1/11	0.0909091
1/12	0.0833333
1/13	0.0769231
1/14	0.0714286
1/15	0.0666667
1/16	0.0625000
1/17	0.0588235
1/18	0.0555556
1/19	0.0526316
1/20	0.0500000
1/21	0.0476190
1/22	0.0454545
1/23	0.0434783
1/24	0.0416667
1/25	0.0400000
1/26	0.0384615
1/27	0.0370370
1/28	0.0357143
1/29	0.0344828
1/30	0.0333333
1/31	0.0322581
1/32	0.0312500
1/33	0.0303030
1/34	0.0294118
1/35	0.0285714
1/36	0.0277778
1/37	0.0270270
1/38	0.0263158
1/39	0.0256410
1/40	0.0250000
1/41	0.0243902
1/42	0.0238095
1/43	0.0232558
1/44	0.0227273
1/45	0.0222222
1/46	0.0217391
1/47	0.0212766
1/48	0.0208333
1/49	0.0204082
1/50	0.0200000
1/51	0.0196078
1/52	0.0192308
1/53	0.0188679
1/54	0.0185185
1/55	0.0181818
1/56	0.0178571
1/57	0.0175439
1/58	0.0172414
1/59	0.0169492
1/60	0.0166667
1/61	0.0163934
1/62	0.0161290
1/63	0.0158730
1/64	0.0156250
1/65	0.0153846
1/66	0.0151515
1/67	0.0149254
1/68	0.0147059
1/69	0.0144928
1/70	0.0142857
1/71	0.0140845
1/72	0.0138889
1/73	0.0136986
1/74	0.0135135
1/75	0.0133333
1/76	0.0131579
1/77	0.0129870
1/78	0.0128205
1/79	0.0126582
1/80	0.0125000
1/81	0.0123457
1/82	0.0121951
1/83	0.0120482
1/84	0.0119048
1/85	0.0117647
1/86	0.0116279
1/87	0.0114943
1/88	0.0113636
1/89	0.0112360
1/90	0.0111111
1/91	0.0109890
1/92	0.0108696
1/93	0.0107527
1/94	0.0106383
1/95	0.0105263
1/96	0.0104167
1/97	0.0103093
1/98	0.0102041
1/99	0.0101010
1/100	0.0100000