asked in 科學數學 · 1 decade ago

微積分一題

(1^2) (2^2) (3^2)

——— +——— +———.................. 

(0!) (1!) (2!)

拜託高手了

Update:

1+Σn/(n-1)!+2Σ1/(n-1)!+Σ1/n!

=1+1+Σ(n+1)/n! [from 1 to infinity]+2e+(e-1)

關鍵我看不懂= =

Σn/(n-1)!=1+Σ(n+1)/n!(???)

2Σ1/(n-1)!=2e(?????)

雖然說這樣講不大好.....

不過我的微積分老師很混= =

所以如果這是很基本的定理的話請和我說一下

大概是哪一單元之類的.............

非常感謝

2 Answers

Rating
  • 1 decade ago
    Favorite Answer

    The original expression is equal to

    1+Σ(n+1)^2/n! [from 1 to infinity]

    =1+Σ(n^2+2n+1)/n!

    =1+Σn/(n-1)!+2Σ1/(n-1)!+Σ1/n!

    =1+1+Σ(n+1)/n! [from 1 to infinity]+2e+(e-1)

    =1+Σ1/(n-1)!+Σ1/n! +3e

    =1+e+(e-1)+3e

    =5e

  • 1 decade ago

    5e

    2009-06-29 23:41:03 補充:

    以版大的程度, 應該看得懂的, 多用心點!

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