text: Class 11
  MATHS
  Arithmetic Progressions
  
  # If a_1,a_2,a_3, ,a_n are an A.P. of non-zero terms, prove that 1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)=
  
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  Text Solution
  
  Solution :
  LHS<br> 1/(a_1a_2)+1/(a_2a_3)+...+1/(a_(n-11)a_n)<br> 1/(a_1(a+1+d))+1/(a_2(a_2+d))+...+1/(a_(n-1)(a_(n-1))+d)<br> 1/d(1/a_1-1/(a_1+d))+1/d(1/(a_2+d))<br> 1/d(1/a_1-1/a_2+1/a_2-1/a_3+...+1/(a_(n-1))-1/a_n)<br> 1/d(1/a_1-1/a_n)<br> 1/d((a_n-a_1)/(a_1a_n))<br> 1/d*((n-1)d)/(a_1a_n)<br> (n-1)/(a_1a_n)<br> RHS.
  
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