Re: [中學] 高中數學問題
※ 引述《poiu716 (宅男6號)》之銘言：
: 已知無窮等比級數的和為16，且前3項的和為18，求此無窮等比級數偶數項的和。
: 小弟資愚鈍，想好久都想不出來求高手解答
: 感謝
原無窮等比級數乘以公比三次方可得到去掉前三項的無窮等比級數
(原來是 a + ar + ar^2 + ar^3 + ar^4 + ...
乘以 r^3 變成 ar^3 + ar^4 + ar^5 + ar^6 + ar^7 + ...)
所以 16 * r^3 = 16 - 18 = -2, 得 r = -1/2
再令奇數項和 P, 偶數項和 Q
P = a + ar^2 + ar^4 + ...
Q = ar + ar^3 + ar^5 + ...
易知 Q = P * r, 又 P+Q = 16, 所以 P = 16/(1+r) = 32, Q = 16 - 32 = -16
--
'You've sort of made up for it tonight,' said Harry. 'Getting the
sword. Finishing the Horcrux. Saving my life.'
'That makes me sound a lot cooler then I was,' Ron mumbled.
'Stuff like that always sounds cooler then it really was,' said
Harry. 'I've been trying to tell you that for years.'
-- Harry Potter and the Deathly Hollows, P.308
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