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Method of iterations

Equation: $ {{x}\over{2}}+\pi =x$

Interval: $ \left[ 0 , 10 \right] $

Initial guess: $ x_0= 8 $

$ i $$ x_i = f(x_{i-1})$
08
17.141592653589793
26.71238898038469
36.497787143782138
46.390486225480862
56.336835766330224
66.310010536754906
76.296597921967246
86.289891614573416
96.286538460876502
106.284861884028044
116.284023595603815
126.2836044513917
136.283394879285643
146.283290093232615
156.283237700206101
166.283211503692844
176.283198405436215
186.283191856307901
196.283188581743744
206.283186944461665
216.283186125820626
226.283185716500106
236.283185511839847
246.283185409509716
256.283185358344651
266.283185332762119
276.283185319970853
286.28318531357522
296.283185310377403
306.283185308778495
316.283185307979041
326.283185307579314
336.28318530737945
346.283185307279518
356.283185307229552
366.283185307204569
376.283185307192078
386.283185307185832
396.283185307182709
406.283185307181148
416.283185307180367
426.283185307179977
436.283185307179782
446.283185307179684
456.283185307179635
466.283185307179611
476.283185307179599
486.283185307179592
496.28318530717959
506.283185307179588
516.283185307179587
526.283185307179586
536.283185307179586
546.283185307179586
556.283185307179586
566.283185307179586
576.283185307179586
586.283185307179586
596.283185307179586
606.283185307179586
616.283185307179586
626.283185307179586
636.283185307179586
646.283185307179586
656.283185307179586
666.283185307179586
676.283185307179586
686.283185307179586
696.283185307179586
706.283185307179586
716.283185307179586
726.283185307179586
736.283185307179586
746.283185307179586
756.283185307179586
766.283185307179586
776.283185307179586
786.283185307179586
796.283185307179586
806.283185307179586
816.283185307179586
826.283185307179586
836.283185307179586
846.283185307179586
856.283185307179586
866.283185307179586
876.283185307179586
886.283185307179586
896.283185307179586
906.283185307179586
916.283185307179586
926.283185307179586
936.283185307179586
946.283185307179586
956.283185307179586
966.283185307179586
976.283185307179586
986.283185307179586
996.283185307179586
1006.283185307179586
1016.283185307179586
1026.283185307179586
1036.283185307179586
1046.283185307179586
1056.283185307179586
1066.283185307179586
1076.283185307179586
1086.283185307179586
1096.283185307179586
1106.283185307179586
1116.283185307179586
1126.283185307179586
1136.283185307179586
1146.283185307179586
1156.283185307179586
1166.283185307179586
1176.283185307179586
1186.283185307179586
1196.283185307179586
1206.283185307179586
1216.283185307179586
1226.283185307179586
1236.283185307179586
1246.283185307179586
1256.283185307179586
1266.283185307179586
1276.283185307179586
1286.283185307179586
1296.283185307179586
1306.283185307179586
1316.283185307179586
1326.283185307179586
1336.283185307179586
1346.283185307179586
1356.283185307179586
1366.283185307179586
1376.283185307179586
1386.283185307179586
1396.283185307179586
1406.283185307179586
1416.283185307179586
1426.283185307179586
1436.283185307179586
1446.283185307179586
1456.283185307179586
1466.283185307179586
1476.283185307179586
1486.283185307179586
1496.283185307179586
1506.283185307179586
1516.283185307179586
1526.283185307179586
1536.283185307179586
1546.283185307179586
1556.283185307179586
1566.283185307179586
1576.283185307179586
1586.283185307179586
1596.283185307179586
1606.283185307179586
1616.283185307179586
1626.283185307179586
1636.283185307179586
1646.283185307179586
1656.283185307179586
1666.283185307179586
1676.283185307179586
1686.283185307179586
1696.283185307179586
1706.283185307179586
1716.283185307179586
1726.283185307179586
1736.283185307179586
1746.283185307179586
1756.283185307179586
1766.283185307179586
1776.283185307179586
1786.283185307179586
1796.283185307179586
1806.283185307179586
1816.283185307179586
1826.283185307179586
1836.283185307179586
1846.283185307179586
1856.283185307179586
1866.283185307179586
1876.283185307179586
1886.283185307179586
1896.283185307179586
1906.283185307179586
1916.283185307179586
1926.283185307179586
1936.283185307179586
1946.283185307179586
1956.283185307179586
1966.283185307179586
1976.283185307179586
1986.283185307179586
1996.283185307179586
2006.283185307179586
2016.283185307179586
2026.283185307179586
2036.283185307179586
2046.283185307179586
2056.283185307179586
2066.283185307179586
2076.283185307179586
2086.283185307179586
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2106.283185307179586
2116.283185307179586
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2136.283185307179586
2146.283185307179586
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2166.283185307179586
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2206.283185307179586
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2246.283185307179586
2256.283185307179586
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2296.283185307179586
2306.283185307179586
2316.283185307179586
2326.283185307179586
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2506.283185307179586
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2606.283185307179586
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2656.283185307179586
2666.283185307179586
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2706.283185307179586
2716.283185307179586
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2756.283185307179586
2766.283185307179586
2776.283185307179586
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2806.283185307179586
2816.283185307179586
2826.283185307179586
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2856.283185307179586
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3106.283185307179586
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3216.283185307179586
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3256.283185307179586
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3306.283185307179586
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3356.283185307179586
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3406.283185307179586
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4506.283185307179586
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4726.283185307179586
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4806.283185307179586
4816.283185307179586
4826.283185307179586
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4916.283185307179586
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