Let \( T_{r} \) and \( S_{r} \) be the \( r^{\text {th }} \) term a...

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Let \( T_{r} \) and \( S_{r} \) be the \( r^{\text {th }} \) term and sum up to \( r^{\text {th }} \) term of a series respectively. If for an odd number \( n, S_{n}= \) \( n \) and \( T_{n}=\frac{T_{n-1}}{n^{2}} \) then \( T_{m} \) (m being even) is
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(A) \( \frac{2}{1+m^{2}} \)
(B) \( \frac{2 m^{2}}{1+m^{2}} \)
(C) \( \frac{(m+1)^{2}}{2+(m+1)^{2}} \)
(D) \( \frac{2(m+1)^{2}}{1+(m+1)^{2}} \)
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