from math import sqrt

x = 1.0
derivative = (sqrt(2) - 1) / 1.0

for i in range(2, 100):
    print sqrt(i), x + derivative, '--', x + derivative - sqrt(i)
    old = derivative
    derivative = (1.0 / (x + derivative)) / 2.0
    x = x + derivative

1.41421356237 1.41421356237 -- 0.0
1.73205080757 1.70710678119 -- -0.0249440263823
2.0 1.93933982822 -- -0.0606601717798
2.2360679775 2.1620859963 -- -0.0739819812004
2.44948974278 2.36678259578 -- -0.0827071470021
2.64575131106 2.55803896408 -- -0.087712346987
2.82842712475 2.73770616643 -- -0.090720958319
3.0 2.90751323108 -- -0.0924867689228
3.16227766017 3.06881510982 -- -0.0934625503472
3.31662479036 3.22270551351 -- -0.0939192768464
3.46410161514 3.37007446706 -- -0.0940271480808
3.60555127546 3.51165467181 -- -0.0938966036517
3.74165738677 3.64805603921 -- -0.0936013475644
3.87298334621 3.77979161457 -- -0.0931917316365
4.0 3.90729716611 -- -0.0927028338918
4.12310562562 4.03094613263 -- -0.0921594929915
4.24264068712 4.15106115229 -- -0.0915795348298
4.35889894354 4.2679230515 -- -0.0909758920394
4.472135955 4.3817779281 -- -0.0903580268979
4.58257569496 4.49284278975 -- -0.0897329052066
4.69041575982 4.60131008541 -- -0.0891056744107
4.79583152331 4.70735138022 -- -0.0884801430967
4.89897948557 4.81112036082 -- -0.08785912475
5.0 4.91275531273 -- -0.0872446872675
5.09901951359 5.0123811775 -- -0.0866383360899
5.19615242271 5.11011127274 -- -0.0860411499662
5.29150262213 5.20604873962 -- -0.0854538825107
5.38516480713 5.30028776835 -- -0.0848770387888
5.47722557505 5.39291464156 -- -0.0843109334894
5.56776436283 5.48400862743 -- -0.0837557353958
5.65685424949 5.57364274792 -- -0.0832115015765
5.74456264654 5.66188444274 -- -0.0826782038022
5.83095189485 5.7487961458 -- -0.0821557490434
5.9160797831 5.83443578767 -- -0.0816439954321
6.0 5.91885723527 -- -0.0811427647261
6.0827625303 6.00211067823 -- -0.0806518520632
6.16441400297 6.08424296936 -- -0.0801710336044
6.2449979984 6.16529792587 -- -0.079700072526
6.32455532034 6.24531659662 -- -0.0792387237149
6.40312423743 6.32433749999 -- -0.0787867374427
6.48074069841 6.40239683618 -- -0.0783438622314
6.5574385243 6.47952867722 -- -0.0779098470795
6.63324958071 6.55576513753 -- -0.0774844431802
6.7082039325 6.63113652726 -- -0.0770674052349
6.78232998313 6.70567149068 -- -0.0766584924456
6.8556546004 6.77939713115 -- -0.0762574692503
6.92820323028 6.85233912442 -- -0.0758641058549
7.0 6.9245218214 -- -0.0754781786023
7.07106781187 6.99596834165 -- -0.0750994702126
7.14142842854 7.06670065862 -- -0.0747277699207
7.21110255093 7.13673967739 -- -0.0743628735338
7.28010988928 7.20610530586 -- -0.0740045834252
7.34846922835 7.27481651987 -- -0.0736527084781
7.4161984871 7.3428914231 -- -0.0733070639924
7.48331477355 7.41034730199 -- -0.0729674715613
7.54983443527 7.47720067634 -- -0.0726337589268
7.61577310586 7.54346734605 -- -0.0723057598188
7.68114574787 7.60916243408 -- -0.0719833137837
7.74596669241 7.67430042641 -- -0.0716662660047
7.81024967591 7.73889520879 -- -0.0713544671185
7.87400787401 7.80296010098 -- -0.0710477730299
7.93725393319 7.86650788847 -- -0.0707460447258
8.0 7.92955085191 -- -0.0704491480917
8.0622577483 7.99210079457 -- -0.0701569537301
8.12403840464 8.05416906785 -- -0.0698693367823
8.18535277187 8.11576659512 -- -0.0695861767552
8.24621125124 8.17690389388 -- -0.0693073573519
8.30662386292 8.23759109661 -- -0.0690327663082
8.36660026534 8.29783797011 -- -0.0687622952337
8.42614977318 8.35765393372 -- -0.0684958394587
8.48528137424 8.41704807635 -- -0.0682332978866
8.54400374532 8.47602917247 -- -0.0679745728517
8.60232526704 8.53460569706 -- -0.0677195699828
8.66025403784 8.59278583977 -- -0.0674681980715
8.71779788708 8.65057751813 -- -0.0672203689465
8.77496438739 8.70798839004 -- -0.0669759973528
8.83176086633 8.76502586549 -- -0.0667350008358
8.88819441732 8.82169711769 -- -0.0664972996306
8.94427191 8.87800909344 -- -0.0662628165555
9.0 8.93396852309 -- -0.0660314769108
9.05538513814 8.98958192976 -- -0.065803208381
9.11043357914 9.0448556382 -- -0.0655779409421
9.16515138991 9.09979578314 -- -0.0653556067722
9.21954445729 9.15440831713 -- -0.0651361401668
9.2736184955 9.20869901804 -- -0.0649194774569
9.32737905309 9.26267349616 -- -0.0647055569311
9.38083151965 9.31633720089 -- -0.0644943187613
9.43398113206 9.36969542713 -- -0.064285704931
9.48683298051 9.42275332134 -- -0.0640796591674
9.53939201417 9.47551588729 -- -0.0638761268761
9.59166304663 9.52798799155 -- -0.0636750550783
9.64365076099 9.58017436864 -- -0.0634763923515
9.69535971483 9.63207962606 -- -0.0632800887719
9.74679434481 9.68370824895 -- -0.0630860958599
9.79795897113 9.73506460461 -- -0.0628943665274
9.8488578018 9.78615294677 -- -0.062704855028
9.89949493661 9.8369774197 -- -0.0625175169085
9.94987437107 9.8875420621 -- -0.062332308963