Group Sequence

Number Theory Level pending

Consider following sequence:

\(1 ,\quad \frac { 1 }{ 2 } ,\quad 1 ,\quad \frac { 1 }{ 3 } ,\quad \frac { 2 }{ 3 } ,\quad 1 ,\quad \frac { 1 }{ 4 } ,\quad \frac { 1 }{ 2 } ,\quad \frac { 3 }{ 4 } ,\quad 1 ,\quad \frac { 1 }{ 5 } ,\quad \frac { 2 }{ 5 } ,\quad \cdots \cdots \)

  1. Find 100th term in the sequence.

  2. Where is \(\frac { 8 }{ 17 } \) in this sequence (which term)?

Let the answer of first question be \(\frac { a }{ b } \) where a and b are coprime, and answer of second question be \( c \).

Evaluate \( \boxed{a+b+c} \)

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