SOLUTION: the answer of a sum is given. write the sum that was asked in sigma notation 8191.5 = 3/2(4^n-1) __________ 3

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Question 1017122: the answer of a sum is given. write the sum that was asked in sigma notation
8191.5 = 3/2(4^n-1)
__________
3
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
8191.5%22%22=%22%22%28expr%283%2F2%29%284%5En-1%29%29%2F3 
Write the denominator 3 as 4-1

8191.5%22%22=%22%22expr%283%2F2%29%284%5En-1%29%2F%284-1%29%29

Compare to the sum formula for a geometric series:

S%5Bn%5D%22%22=%22%22a%5B1%5D%28r%5En-1%29%2F%28r-1%29%29%22%22=%22%22sum%28a%5B1%5D%2Ar%5Ek%2Ck=1%2Cn%29 

a%5B1%5D%22%22=%22%223%2F2, r%22%22=%22%224

Also solve for n

8191.5%22%22=%22%22expr%283%2F2%29%284%5En-1%29%2F3%29

Multiply both sides by 3

8191%2A3%22%22=%22%22expr%283%2F2%29%284%5En-1%29

Multiply both sides by 2

8191.5%2A3%2A2%22%22=%22%22expr%283%29%284%5En-1%29

Divide both sides by 3

8191.5%2A2%22%22=%22%224%5En-1

16383%22%22=%22%224%5En-1

16384%22%22=%22%224%5En

4%5E7%22%22=%22%224%5En

7%22%22=%22%22n

Substitute in 

sum%28a%5B1%5D%2Ar%5Ek%2Ck=1%2Cn%29

sum%28%28expr%283%2F2%29%2A4%5Ek%29%2Ck=1%2Cn%29

Edwin