14/08/16 05:45:29.15
>>217
書き間違えた。u_[n]が全部u_[n+1]だ
＞X_[n+1]^2=(X_[n]+u_[n+1])^2
＞X_[n+1]^2=X_[n]^2+2X_[n]u_[n+1]+u_[n+1]^2
＞E(X_[n+1]^2)
＞=E(X_[n]^2+2X_[n]u_[n+1]+u_[n+1]^2)
＞=E(X_[n]^2)+2E(X_[n])E(u_[n+1])+E(u_[n+1]^2)
多分めちゃくちゃ綺麗に値でるし、作問者は漸化式作って欲しかったと思うよ
E(X_[n])=(1/2)^n-(1/4)^n
E(u_[n+1])
=(1/2)^(n+1)[3(1/2)^(n+1)-1]
=[(3/2)(1/4)^n-(1/2)^n]×(1/2)
E(u_[n+1]^2)
=a_[n+1]^2=[(1/2)^(n+1)]^2
=(1/4)×(1/4)^n
E(X_[n+1]^2)=E(X_[n]^2)+2E(X_[n])E(u_[n+1])+E(u_[n+1]^2)より
E(X_[n+1]^2)=E(X_[n]^2)-(3/4)(1/4)^n+(5/2)(1/8)^n-(3/2)(1/16)^n
後はこれ解いてn→無限大とるだけだからな。