Sequences and Series


   
 
To insert n Harmonic Means between two given quantities
Let a and b be two given quantities. It is required to insert n harmonic means h1, h2, h3,....hn between the quantities a and b.
 
 
 
Let d = common difference of the A.P.
 
 
 
 
 
 
Hence h1, h2,....hn are the n harmonic means.
 
If A, G and H respectively are arithmetic, geometric and harmonic means of two positive quantities a and b, then

G2 = A.H and A ≥G≥H

 
 
            
 
             
 
             
 
             
 
              
 
              
  
               
 
  
     
   
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