? 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

Relevance
• rotchm
Lv 7
2 months ago

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.

• 2 months ago

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