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    				| 1. | Insert three harmonic between `(1)/(12) and (1)/(20)`. | 
| Answer» After inserting the harmonic means, let the harmonic progression be, `(1)/(a) , (1)/(a+d) , (1)/(a+2d), (1)/(a+3d), (1)/(a+4d)` Given, `(1)/(a) = (1)/(12) and (1)/(a+4d) = (1)/(20)rArr a = 12 and d = 2` `therefore ` The required harmonic means are `(1)/(14), (1)/(16) and (1)/(18)`. | |