i f space t h e space c o m m o n space r a t i o space o f space a space G P space w i t h space a space s u m space t o space infinity space i s space x squared space minus space x minus 1 comma space w i t h i n space w h a t space l i m i t space m u s t space x space l i e ?

Asked by Olivia Adhikary | 19th Aug, 2014, 11:33: AM

Expert Answer:

F o r space I n f i n i t e space G P comma space 0 less or equal than r less or equal than 1 G i v e n space r equals x squared minus x minus 1  c a s e space 1 : space r greater or equal than 0 x squared minus x minus 1 greater or equal than 0 rightwards double arrow x greater or equal than fraction numerator 1 plus square root of 5 over denominator 2 end fraction o r space space x less or equal than fraction numerator 1 minus square root of 5 over denominator 2 end fraction  C a s e space 2 : space x squared minus x minus 1 less or equal than 1 x squared minus x minus 2 less or equal than 0 open parentheses x minus 2 close parentheses open parentheses x plus 1 close parentheses less or equal than 0 rightwards double arrow minus 1 less or equal than x less or equal than 2  I n t e r s e c t i o n space i s space x element of open square brackets minus 1 comma fraction numerator 1 minus square root of 5 over denominator 2 end fraction close square brackets space union open square brackets fraction numerator 1 plus square root of 5 over denominator 2 end fraction comma 2 close square brackets

Answered by Dharma Teja | 19th Aug, 2014, 03:47: PM

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