question_answer

If\[x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}},y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}},z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}},\]where a, b, c are in AP and\[|a|<1,|b|<1,|c|<1,\]then\[x,\text{ }y,\text{ }z\]are in     AIEEE  Solved  Paper-2005

A) HP  

B)                       AGP      

C)        AP                         

D)        GP         

Correct Answer: A

Solution :

Since,                                                        ?.(i) Similarly,and                 ...(ii)                                 Now, a, b, c are in AP.  are also in AP. \[1-a,\,\,1-b,\,1-c\] are also in AP. are in HP. are in HP. Alternate Solution Since, [from Eqs. (i) and (ii)]    are in AP.       are in HP.