鯨魚
Lv 4
鯨魚 發問時間: 科學數學 · 8 年前

要怎麼解出這些微積分的難題?

這些微積分好難,請各位厲害的數學大大指導我一下。

圖片參考:http://imgcld.yimg.com/8/n/AE02661996/o/1612032300...

1 個解答

評分
  • 阿銘
    Lv 7
    8 年前
    最佳解答

    1.An=(n-1)/n-n/(n-1)

    (n-1)/n-n/(n-1)=1-(1/n)-1+1/(n-1)=1/(n-1)-1/n=(n-n+1)/n(n-1)=1/n(n-1)

    limAn=0

    n approach infinity

    the sequence converges

    summationA2+A3+------=(1-1/2)+(1/2-1/3)+-----------------=1

    -------------------------------------------------------------------------------------------------------------

    2.ln[(n+1)/n]=ln(1+1/n)

    limAn =ln1=0

    n approach infinity

    th e sequence converges

    ---------------------------------------------------------------------------------------------------------------

    4 1/200+1/210+1/220+-----

    An=1/[200+10(n-1)].

    lim An=0

    n approach infinity

    the sequence converges

    -------------------------------------------------------------------------------------------------------------+

    5.An=(-1)^n*2*4*6*----(2n)/2*5*8*-------------(3n-10)

    limit l A(n+1)/(An)l=l(-1)*(2n+2)/(3n+3)l=l(-1)*2/3l<1

    n approaches infinuty

    the sequence converges

    --------------------------------------------------------------------------------------------------------------

    6.1+2/3+3/3^2+4/3^3+------------=

    An=n/3^(n-1)

    limit A(n+1)/An=[(n+1)/3^n]/[n/3^(n-1)]=[(n+1)/n]*1/3=1/3*(1+1/n)=1/3<1

    n approaches infinity

    the sequence converges

    -------------------------------------------------------------------------------------------------------------

    7.Stan^4(x/2)*sec^4(x/2)dx=Stan^4(*x/2)*sec^2(x/2)*sec^2xdx

    =Stan^4(x/2)*[1+tan^2(x/2)]*sec^2(x/2)dx

    =Stan^4(x/2)*sec^2(x/2)+tan^6(x/2)*sec^2(x/2)dx

    =1/5*2*tan^5(x/2)+1/7*2*tan^7(x/2)+c

    =2/5*tan^5(x/2)+2/7tan^7(x/2)+c

    2012-03-24 18:35:12 補充:

    3.use the Integral test

    ∑(n=1~∞) 1/n(lnn)^1/2

    ∫(x=1~∞) 1/x(lnx)^1/2dx let lnx=u then x=e^u 1/x dx=du

    ∫(u=0~∞) u^-1/2du=2*u^1/2l(u=0~∞) =∞

    the sequence diverges

    • Commenter avatar登入以對解答發表意見
還有問題?馬上發問,尋求解答。