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8 5 ⋄ 13 8 ⋄ 21 13 ⋄ 34 21 ⋄ … {\displaystyle {\frac {8}{5}}\diamond {\frac {13}{8}}\diamond {\frac {21}{13}}\diamond {\frac {34}{21}}\diamond \ldots }
= 5 8 − 5 8 {\displaystyle ={\sqrt {{\frac {5}{8}}-{\frac {\sqrt {5}}{8}}}}} = 1 2 1 2 ( 5 − 5 ) {\displaystyle ={\frac {1}{2}}{\sqrt {{\frac {1}{2}}(5-{\sqrt {5}})}}}
= 5 8 + 5 8 {\displaystyle ={\sqrt {{\frac {5}{8}}+{\frac {\sqrt {5}}{8}}}}} = 1 2 1 2 ( 5 + 5 ) {\displaystyle ={\frac {1}{2}}{\sqrt {{\frac {1}{2}}(5+{\sqrt {5}})}}}
= 3 − 1 2 2 {\displaystyle ={\frac {{\sqrt {3}}-1}{2{\sqrt {2}}}}}
= 3 + 1 2 2 {\displaystyle ={\frac {{\sqrt {3}}+1}{2{\sqrt {2}}}}}