? asked in Science & MathematicsMathematics · 2 months ago

 Use the summation formulas to rewrite the expression without the summation notation.?

 

n

 Σ  (4i + 7)/(n^2)

i = 1

 

S(n) =

Use the result to find the sums for n = 10, 100, 1000, and 10,000.

n =    10   

n =    100   

n =    1,000   

n =    10,000  

Update:

I knew alreadt the s(n)= 2+9/n but i did not know how to find the rest

2 Answers

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  • rotchm
    Lv 7
    2 months ago
    Favorite Answer

    n

     Σ (4i + 7)/(n^2)

    i = 1

    = (4Σi + 7Σ1) / n².

    Σi = n(n+1)/2.  Σ1 = [left for you. that's a trivial one].

    So, what expression do you finally get ?

    Answer that & we will take it from there if need be. 

    Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them. 

  • 4 * 1 + 7 + 4 * 2 + 7 + 4 * 3 + 7 + 4 * 4 + 7 + ... + 4 * n + 7 =>

    4 * (1 + 2 + 3 + 4 + ... + n) + 7 * n =>

    4 * (1/2) * n * (n + 1) + 7n =>

    2 * (n^2 + n) + 7n =>

    2n^2 + 2n + 7n =>

    2n^2 + 9n

    (2n^2 + 9n) / n^2 =>

    2 + 9/n

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