Could someone please check my work

Prove : If ( Sn) and ( Sn+ TA) are convergent Sequences, Then ( Tn ) converges . Suppose (S) and (sn+ in) org convergent sequences. by Theorem 4.2. 1 ( a ) , Ler ( Sm) -5 and ( Sn+ T.) - 5+1 By The definition of convergence, VETO INEN Such That VAIN, / SA- 5/ 6 5 0 and VETO IN, EIN Such That VnIN2, SA + TA - ( 5 + 1) ) = / Sn+ TA - 5- T/