import numpy as np
import sympy as sp
import matplotlib.pyplot as plt
from IPython.display import display
import japanize_matplotlib

n=sp.var('n',integer=True)
a = sp.Function('a')
f = a(n)-sp.Rational(1,2)*a(n-1)-3
display('漸化式は',f)
ans=sp.rsolve(f, a(n), {a(1):2})
display('一般項は',ans)
lim_an = sp.limit(ans, n, sp.oo)
display('n→∞のときの極限値は',lim_an)