1. Compute the value and the successive convergents of the following finite continued fractions:
(i) $\langle 1,2,3\rangle$;
(ii) $\langle 0,1,2,3\rangle$;
(iii) $\langle 3,2,1\rangle$;
(iv) $\langle 2,1,1,4,1,1\rangle$;
(v) $\langle-4,2,1,7,8\rangle$;
(vi) $\langle-1,1 / 2,1 / 3\rangle$;
(vii) $\langle 1 / 2,1 / 4,1 / 8,1 / 16\rangle$.
1. (i) $10 / 7$; Nearest fractions are: $1,3 / 2,10 / 7$.
(ii) $7 / 10$; Nearest fractions are: $0,1,2 / 3,7 / 10$.
(iii) $10 / 3$; Nearest fractions are: $3,7 / 2,10 / 3$.
(iv) $51 / 20$; Nearest fractions are: $2,3,5 / 2,23 / 9,28 / 11,51 / 20$.
(v) $-683 / 187$; Nearest fractions are: $-4,-7 / 2,-11 / 3,-84 / 23,-683 / 187$.
(vi) $-5 / 7$; Nearest fractions are: $-1,1,-5 / 7$.
(vii) $1193 / 322$; Nearest fractions are: $1 / 2,9 / 2,41 / 66,1193 / 322$.