Oils fractions

Oils fractions

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shell lubricants locator | shell global skip to main content home - shell global menu home motorists motorists view motorists motorists view motorists shell fuels shell engine oils and lubricants shell engine oils and lubricants view shell engine oils and lubricants motorists shell engine oils and lubricants
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shell rimula truck & light duty oils | shell global skip to main content home - shell global menu home motorists motorists view motorists motorists view motorists shell fuels shell engine oils and lubricants shell engine oils and lubricants view shell engine oils and lubricants motorists shell engine
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approximating square root ask question asked today active today viewed times $egingroup$ we define recursive sequences $a_{n+ }= + rac { +a_n}$, $a_ = $ and $b_{n+ }= rac{b_n^ + }{ b_n}$, $b_ = $. i wish to show that $b_{n+ }=a_{ ^n}$. this can be proven using closed forms expressions related to continued fractions
be expressed as $$a_n=\sqrt \cdot rac{( +\sqrt )^n +( -\sqrt )^n}{( +\sqrt )^n - ( -\sqrt )^n}$$ on the other hand, we can prove inductively that $$ rac{b_{n+ }-\sqrt }{b_{n+ }+\sqrt }=\left( rac{ -\sqrt }{ +\sqrt } ight)^{ ^n}$$ so the relation $a_{ ^n}=b_{n+ }$ can be deduced by expanding the fractions...
https://math.stackexchange.com/questions/3491183/relation-between-two-rational-sequences-approximating-square-root-2
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hygrometer educational models anatomical models organ models reproductive models skeleton models system models torso models zoology models & botany model electronics general physics geography & working models math lab abacus place value allotting base ten block board game circle cubes date & finance fractions
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hygrometer educational models anatomical models organ models reproductive models skeleton models system models torso models zoology models & botany model electronics general physics geography & working models math lab abacus place value allotting base ten block board game circle cubes date & finance fractions
hygrometer educational models anatomical models organ models reproductive models skeleton models system models torso models zoology models & botany model electronics general physics geography & working models math lab abacus place value allotting base ten block board game circle cubes date & finance fractions...
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hygrometer educational models anatomical models organ models reproductive models skeleton models system models torso models zoology models & botany model electronics general physics geography & working models math lab abacus place value allotting base ten block board game circle cubes date & finance fractions
hygrometer educational models anatomical models organ models reproductive models skeleton models system models torso models zoology models & botany model electronics general physics geography & working models math lab abacus place value allotting base ten block board game circle cubes date & finance fractions...
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