SOLUTION: Write geometric series -9/2+3/2-1/2+1/6- ••• + 1/39366 in summation notation. Using the formula for the sum of an geometric series, compute the sum in the problem above.

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Question 1131912: Write geometric series -9/2+3/2-1/2+1/6- ••• + 1/39366 in summation notation. Using the formula for the sum of an geometric series, compute the sum in the problem above.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
geometric series -9/2+3/2-1/2+1/6- ••• + 1/39366
-the first term
-the "common ratio" between terms
-the nth term








sum:


...we need

use last given term and plug it in

...last given term is

...solve for



...take log of both sides















=>















Answer by ikleyn(52772)   (Show Source): You can put this solution on YOUR website!
.

            The solution by  @MathLover1  seems to be almost infinitely long;
            but it can be implemented much shorter,  without making unnecessary calculations.
            See my solution below. 


The common ratio is  q =  :  =  =  = .


The formula for the sum of "n" first term of an geometry progression is


    S = .


We have   =   and   =   (the n-th term).


Therefore,  


    S =  =  =  =  =  =  =  = .


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