Re: [極限]

[Honor1984 (希望願望成真)]

※ 引述《Qmmm (Q蛆蛆)》之銘言：
: 設a_1+ a_2+ ....+ a_n= 3n^2
: 求 lim   [ √(a_2+ a_4+ ...+ a_(2n))- √(a_1+ a_3+ a_5+ ...+ a_(2n-1))]= ?
:    n→∞

令A = a_2+ a_4+ ...+ a_(2n)

 B = a_1+ a_3+ a_5+ ...+ a_(2n-1)

 a_1 + ... + a_2n =  12n^2 = A + B

 a_n = 3[(n)^2 - (n-1)^2] = 3(2n-1)

 A = Σ3[2*2k-1] = 6(n+1)n - 3n = 6n^2 + 3n

求lim √A - √B

= lim √A - √(12n^2-A)

        2A -12n^2
= lim ------------
      √A + √(12n^2-A)

         6n
= lim ------------
       √A + √(12n^2-A)

         6
=    -----------
     √6 + √6

=  √6 /2

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推 andy2007:請問 a_1 + ... + a_2n =  12n^2 = A + B
→ andy2007:和 a_n = 3[(n)^2 - (n-1)^2] = 3(2n-1)
→ andy2007:這兩行是怎麼來的呢 ? 程度差 煩請指導