x1=1/2^0+1=1
は 1/2^0=1
なので間違ってますよね?
以下の漸化式で表される数列を求める問題と解釈して、数列を生成するサンプルコードを記載しました。意図とあっていますでしょうか?
python
1import matplotlib.pyplot as plt
2import numpy as np
3
4terms = [] # 数列
5num_terms = 20 # 何項まで計算するか
6
7# 初項
8p = np.zeros(3, dtype=float)
9terms.append(p)
10
11# 第1項から num_terms 項まで計算
12for i in range(1, num_terms + 1):
13 p = 0.5 ** p + np.array([1, 2, 3])
14 terms.append(p)
15terms = np.array(terms)
16
17# 数列を表示
18for i, p in enumerate(terms):
19 print('P_{}: ({:.15f}, {:.15f}, {:.15f})'.format(i, *p))
20
21import matplotlib.pyplot as plt
22
23# 描画
24plt.plot(np.arange(num_terms + 1), terms[:, 0], 'p-', label='x')
25plt.plot(np.arange(num_terms + 1), terms[:, 1], 'p-', label='y')
26plt.plot(np.arange(num_terms + 1), terms[:, 2], 'p-', label='z')
27plt.legend()
28plt.show()
P_0: (0.000000000000000, 0.000000000000000, 0.000000000000000)
P_1: (2.000000000000000, 3.000000000000000, 4.000000000000000)
P_2: (1.250000000000000, 2.125000000000000, 3.062500000000000)
P_3: (1.420448207626857, 2.229251010801168, 3.119700410087322)
P_4: (1.373596227548015, 2.213269415102580, 3.115047344568156)
P_5: (1.385928039773987, 2.215645061885113, 3.115419001102066)
P_6: (1.382643277854366, 2.215290257216088, 3.115389271533550)
P_7: (1.383515481597683, 2.215343210459798, 3.115391649380914)
P_8: (1.383283691416893, 2.215335306563332, 3.115391459192762)
P_9: (1.383345276527280, 2.215336486294725, 3.115391474404633)
P_10: (1.383328912807562, 2.215336310208233, 3.115391473187938)
P_11: (1.383333260727452, 2.215336336490862, 3.115391473285253)
P_12: (1.383332105459187, 2.215336332567922, 3.115391473277469)
P_13: (1.383332412420520, 2.215336333153459, 3.115391473278092)
P_14: (1.383332330859128, 2.215336333066062, 3.115391473278042)
P_15: (1.383332352530457, 2.215336333079107, 3.115391473278046)
P_16: (1.383332346772261, 2.215336333077160, 3.115391473278045)
P_17: (1.383332348302247, 2.215336333077451, 3.115391473278045)
P_18: (1.383332347895721, 2.215336333077407, 3.115391473278045)
極限はすぐにはわからなかったですが、見た感じ収束列っぽいですね