08/11/24 21:48:14
>>42
中略の計算部分はこれでいいのでしょうか？
(D(a*f＋b*g))(n)
=(a*f＋b*g)(n＋1)-(a*f＋b*g)(n)
=a*f(n＋1)＋b*g(n＋1)-a*f(n)-b*g(n)
=a*(f(n＋1)-f(n))＋b*(g(n＋1)-g(n))
=a(D(f))(n)＋b(D(g))(n)
(D'(a*f＋b*g))(n)
=(a*f＋b*g)(1)＋(a*f＋b*g)(2)＋…＋(a*f＋b*g)(n)
=a*f(1)＋b*g(1)＋a*f(2)＋b*g(2)＋…＋a*f(n)＋b*g(n)
=Σ[k=1,n]a*f(k)＋Σ[k=1,n]b*g(k)
=a(D'(f))(n)＋b(D'(g))(n)
((D◦D')(f))(n)
=(D(D'f))(n)
=(D'f)(n＋1)-(D'f)(n)
=Σ[k=1,n＋1]f(k)-Σ[k=1,n]f(k)
=f(n＋1)
((D'◦D)(f))(n)
=(D'(Df))(n)
=(D(f))(1)＋(D(f))(2)＋…＋(D(f))(n)
=(f(2)-f(1))＋(f(3)-f(2))＋…＋(f(n＋1)-f(n))
=f(n＋1)-f(1)