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  • 觀察下列一串單項(xiàng)式的特點(diǎn):xy,-2x2y,4x3y,-8x4y,16x5y,… (1)按此規(guī)律寫出第9個(gè)單項(xiàng)式; (2)試猜想第N個(gè)單項(xiàng)式為多少?它的系數(shù)和次數(shù)分別是多少?

    觀察下列一串單項(xiàng)式的特點(diǎn):xy,-2x2y,4x3y,-8x4y,16x5y,…
    (1)按此規(guī)律寫出第9個(gè)單項(xiàng)式;
    (2)試猜想第N個(gè)單項(xiàng)式為多少?它的系數(shù)和次數(shù)分別是多少?
    數(shù)學(xué)人氣:121 ℃時(shí)間:2019-09-18 02:14:07
    優(yōu)質(zhì)解答
    (1)∵當(dāng)n=1時(shí),xy,
    當(dāng)n=2時(shí),-2x2y,
    當(dāng)n=3時(shí),4x3y,
    當(dāng)n=4時(shí),-8x4y,
    當(dāng)n=5時(shí),16x5y,
    ∴第9個(gè)單項(xiàng)式是29-1x9y,即256x9y.
    (2)∴n為偶數(shù)時(shí),單項(xiàng)式為負(fù)數(shù).x的指數(shù)為n時(shí),2的指數(shù)為n-1,
    ∴當(dāng)n為奇數(shù)時(shí)的單項(xiàng)式為2n-1xny,
    它的系數(shù)是2n-1,次數(shù)是n+1.
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