IIT JEE , AIEEE Forum - Mathematics , Algebra

neal

x= _{[n=1 ]}

^{[infinity ]} aⁿy= _{[n=1 ]}

^{[infinity ]} bⁿ

z=_{[n=1 ]}

^{[infinity ]} cⁿ
if a,b,c are in AP then x,y,z are in

A)AP
B)HP
C)GP
D)None of these....

can any1 give a clear explanation

shakirshafi12

well there is something missing in the question

a,b,c <1

----the series started frm n=0 but in ur question n=1------

----pls check these details are missing------------

using G.P formula for infinite series

x=a/(1-a)

y=b/(1-b)

z=c/(1-c)

a=x/(1+x)=1-1/(1+x)

b=y/(1+y)=1-1/(1+y)

c=z/(1+z)=1-1/(1+z)

a,b,c are in A.P

so

1-1/(1+x),1-1/(1+y),1-1/(1+z) are also in A.P

1/(1+x),1/(1+y),1/(1+z) are in A.P

1+x,1+y,1+z are hence in H.P

neal

thnxalot...i got it....