填充2
自\(P_1(1,0)\)作\(x\)軸的垂直線交拋物線\(y=x^2\)於\(Q_1(1,1)\),再由\(Q_1\)作此拋物線的切線交\(x\)軸於\(P_2\),又自\(P_2\)作\(x\)軸的垂線交此拋物線於\(Q_2\),如此依序進行,試求級數\(\overline{P_1Q_1}+\overline{P_2Q_2}+\ldots+\overline{P_nQ_n}+\ldots\)之和。
[解答]
牛頓法
等比級數1+1/4+1/16=....=1/(1-1/4)=4/3
113.5.4補充
自\(P_1(1,0)\)作\(x\)軸的垂直線交拋物線\(y=x^2\)於\(Q_1(1,1)\),再由\(Q_1\)作此拋物線的切線交\(x\)軸於\(P_2\),又自\(P_2\)作\(x\)軸的垂線交此拋物線於\(Q_2\),如此依序進行,試求級數\(\overline{P_1Q_1}+\overline{P_2Q_2}+\ldots+\overline{P_nQ_n}+\ldots\)之和。
(113全國高中職聯招,
https://math.pro/db/thread-3859-1-1.html)