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Math Help - Real analysis homework help!!!!!!

  1. #1
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    Real analysis homework help!!!!!!

    Suppose that (sn) and (tn) are convergent sequences with
    lim sn =s and lim tn =t. Then lim (sntn)= st. Prove this without using the identity
    sntn-st= (sn-s)(tn-t) +s(tn-t)+t(sn-s).
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  2. #2
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    This is the complete solution.
    \left| {s_n t_n  - ST} \right| \leqslant \left| {s_n t_n  - St_n } \right| + \left| {St_n  - ST} \right| \leqslant \left| {t_n } \right|\left| {s_n  - S} \right| + \left| S \right|\left| {t_n  - T} \right|
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