Finding a of n from Sn partial sum

  • #1

Homework Statement



suppose that the partial sum of the series (sigma)n=1,infinity an is given by the partial sum Sn = (-2n+9)/(-6n+15). Find an expression for an when n>1

Homework Equations



Sn= (-2n+9)/(6n+15

The Attempt at a Solution


So I attempted to subtract S(n-1) from S(n) to get each term for an and got the following terms
a2=8/9
3=-8/3
4=8/9
5=8/45
6=8/105
7=8/189
8=8/297
How am I supposed to come up with a generalized expression from these terms, or am I wrong from the first step of doing S(n)-S(n-1) to get those terms for an? The only pattern I can recognize is that after a4, the difference of the denominators increase by 24 from one term to the next.

Homework Statement





Homework Equations





The Attempt at a Solution

 
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Answers and Replies

  • #2
Dick
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Homework Statement



suppose that the partial sum of the series (sigma)n=1,infinity an is given by the partial sum Sn = (-2n+9)/(6n+15). Find an expression for an when n>1

Homework Equations



Sn= (-2n+9)/(6n+15

The Attempt at a Solution


So I attempted to subtract S(n-1) from S(n) to get each term for an and got the following terms
a2=8/9
3=-8/3
4=8/9
5=8/45
6=8/105
7=8/189
8=8/297
How am I supposed to come up with a generalized expression from these terms, or am I wrong from the first step of doing S(n)-S(n-1) to get those terms for an? The only pattern I can recognize is that after a4, the difference of the denominators increase by 24 from one term to the next.

Homework Statement





Homework Equations





The Attempt at a Solution

##S_{n}-S_{n-1}=a_n##. So take your expression for ##S_n## and subtract the same expression with n-1 substituted for n. Putting numbers in isn't the way to do it.
 
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