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.