Question 314463
{{{Sn=(2n*2)/((n*n)+1)}}}
{{{S1=(2*1*2)/(1+1)=4/2=2}}}
{{{S2=(2*2*2)/(4+1)=8/5}}}
{{{S3=(2*3*2)/(9+1)=12/10=6/5}}}
Those are the sums of terms.
The first term is equal to the first sum.
{{{a1=2}}}
.
.
{{{S2=a1+a2=8/5}}}
{{{2+a2=8/5}}}
{{{a2=8/5-10/5}}}
{{{a2=-2/5}}}
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.
{{{S3=a1+a2+a3=8/5+a3}}}
{{{8/5+a3=6/5}}}
{{{highlight(a3=-2/5)}}}