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  • 做個(gè)題lim[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) n→∞

    做個(gè)題lim[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) n→∞
    數(shù)學(xué)人氣:486 ℃時(shí)間:2020-05-22 04:44:16
    優(yōu)質(zhì)解答
    1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2)=1/3*(1/2-1/5+1/5-1/8+...+1/(3n-1)-1/(3n+2))
    =1/3*(1/2-1/(3n+2))
    所以lim(n→∞)[1/2×5 +1/5×8+1/8×11.+1/(3n-1)(3n+2) ]
    =lim(n→∞)[1/3*(1/2-1/(3n+2))]
    =1/3*(lim(n→∞)1/2-lim(n→∞)(1/(3n=2))
    =1/3*(1/2-0)
    =1/6
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