[" Then "16(lim_(n rarr oo)(s_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)......+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+......+S_(n)^(2)))" is "]

Let S_(n),n=1,2,2.... be the sum of infinite geometric series whose first term is n and the common ratio is.(1)/(n+1) .Evaluate lim_(n rarr oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+....+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+...+S_(n)^(2))

Let S_(n),n=1,2,3,"…" be the sum of infinite geometric series, whose first term is n and the common ratio is (1)/(n+1) . Evaluate lim_(n to oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+"..."+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+"......"+S_(n)^(2)) .

Let S_(n),n=1,2,3,"…" be the sum of infinite geometric series, whose first term is n and the common ratio is (1)/(n+1) . Evaluate lim_(n to oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+"..."+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+"......"+S_(n)^(2)) .

Let S_(n),n=1,2,3,"…" be the sum of infinite geometric series, whose first term is n and the common ratio is (1)/(n+1) . Evaluate lim_(n to oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+"..."+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+"......"+S_(n)^(2)) .

Let S_(n),n=1,2,3,"…" be the sum of infinite geometric series, whose first term is n and the common ratio is (1)/(n+1) . Evaluate lim_(n to oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+"..."+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+"......"+S_(n)^(2)) .

S_(n+3)-3S_(n+2)+3S_(n+1)-S_(n)=0

S_(n) = (1+2+3+....+n)/( n) then S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ..... + S_(n)^(2) =

Find lim_(n rarr oo)S_(n); if S_(n)=(1)/(2n)+(1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-4))+......+(1)/(sqrt(3n^(2)+2n-1))

S_(N^(1))and S_(N^(2)) reactions are

If S_(1), S_(2) and S_(3) denote the sum of first n_(1) , n_(2) and n_(3) terms respectively of an A.P.L , then : (S_(1))/(n_(1)) . ( n _(2) - n_(3)) + ( S_(2))/( n_(2)). ( n _(3) - n_(1)) + ( S_(3))/( n_(3)) . ( n_(1) - n_(2)) is equal to :