If \({\rm{A}} = {\rm{}}\frac{1}{{1{\rm{\;}} \times {\rm{\;}}2}}{\rm{}} + {\rm{}}\frac{1}{{1{\rm{\;}} \times {\rm{\;}}4}}{\rm{}} + {\rm{}}\frac{1}{{2{\rm{\;}} \times {\rm{\;}}3}}{\rm{}} + {\rm{}}\frac{1}{{4{\rm{\;}} \times {\rm{\;}}7}}{\rm{}} + {\rm{}}\frac{1}{{3{\rm{\;}} \times {\rm{\;}}4}}{\rm{}} + {\rm{}}\frac{1}{{7{\rm{\;}} \times {\rm{\;}}10}} - - - \) upto 20 terms, then what is the value of A?

1
379/308
2
171/140
3
379/310
4
420/341

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