已知两点\(O(0,0)\)，\(Q(a,b)\)，点\(P_{1}\)是线段\(OQ\)的中点，点\(P_{2}\)是线段\(QP_{1}\)的中点，\(P_{3}\)是线段\(P_{1}P_{2}\)的中点，\(┅\)，\(P_{n+2}\)是线段\(P_{n}P_{n+1}\)的中点，则点\(P

已知两点\(O(0,0)\)，\(Q(a,b)\)，点\(P_{1}\)是线段\(OQ\)的中点，点\(P_{2}\)是线段\(QP_{1}\)的中点，\(P_{3}\)是线段\(P_{1}P_{2}\)的中点，\(┅\)，\(P_{n+2}\)是线段\(P_{n}P_{n+1}\)的中点，则点\(P_{n}\)的极限位置应是\((\)　　\()\)

A．\(( \dfrac {a}{2}, \dfrac {b}{2})\)

B．\(( \dfrac {a}{3}, \dfrac {b}{3})\)

C．\(( \dfrac {2a}{3}, \dfrac {2b}{3})\)

D．\(( \dfrac {3a}{4}, \dfrac {3b}{4})\)

【考点】中点坐标公式,定积分的概念及几何意义

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难度：较难

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