SOLUTION: the sum of the first n terms,Sn of a series is given by Sn=2n*2/(n*n)+1,then is the third term is 9/5?

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Question 314463: the sum of the first n terms,Sn of a series is given by Sn=2n*2/(n*n)+1,then
is the third term is 9/5?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Sn=%282n%2A2%29%2F%28%28n%2An%29%2B1%29
S1=%282%2A1%2A2%29%2F%281%2B1%29=4%2F2=2
S2=%282%2A2%2A2%29%2F%284%2B1%29=8%2F5
S3=%282%2A3%2A2%29%2F%289%2B1%29=12%2F10=6%2F5
Those are the sums of terms.
The first term is equal to the first sum.
a1=2
.
.
S2=a1%2Ba2=8%2F5
2%2Ba2=8%2F5
a2=8%2F5-10%2F5
a2=-2%2F5
.
.
S3=a1%2Ba2%2Ba3=8%2F5%2Ba3
8%2F5%2Ba3=6%2F5
highlight%28a3=-2%2F5%29