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how ? reciprocal of any natural number lies between 0 and 1 ??? how ???
Asked by diya_shukl | 17 Apr, 2015, 07:14: PM
answered-by-expert Expert Answer
C o n s i d e r space a n y space n a t u r a l space n u m b e r. L e t space n space b e space a space n a t u r a l space T h e space r e c i p r o c a l space o f space a n y space n u m b e r space i s space 1 over n. T h a t space i s space t h e space n u m e r a t o r space o f space t h e space r e c i p r o c a l space o f space t h e space n a t u r a l space n u m b e r space i s space a l w a y s space 1 space a n d space t h e d e n o m i n a t o r space o f space t h e space r e c i p r o c a l space o f space t h e space n a t u r a l space n u m b e r space i s space n. I f space n equals 1 comma space t h e n comma space t h e space r e c i p r o c a l space o f space 1 space i s space o n e space i t s e l f. I f space n equals 2 comma space t h e n space t h e space r e c i p r o c a l space o f space 2 space i s space 1 half W e space k n o w space t h a t comma space 1 half equals 0.5 space A n d space 0.5 less than 1 I f space y o u space i n c r e a s e space t h e space d e n o m i n a t o r comma space t h e space v a l u e space o f space t h e space f r a c t i o n space d e c r e a s e s. T h a t space i s comma space 1 greater than 1 half greater than 1 third greater than 1 fourth greater than 1 fifth greater than... greater than 1 over n greater than... greater than fraction numerator 1 over denominator 2 n end fraction... greater than 0 T h e r e f o r e comma space t h e space r e c i p r o c a l space o f space a n y space n a t u r a l space n u m b e r space a l w a y s space l i e s space b e t w e e n comma space 0 space a n d space 1 T h a t space i s comma space 0 less than 1 over n less than 1 comma space n greater than 1.
Answered by Vimala Ramamurthy | 19 Apr, 2015, 01:00: PM

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