Question

If ( x=sum_{n=0}^{infty} a^{n}, y=sum_{n=0}^{infty} b^{n}, z=sum_{n=0}^{infty} c^{n} ) where ( a, b, c ) are in A.P.
and ( |mathrm{a}|<1,|mathrm{b}|<1,|mathrm{c}|<1 ) then ( mathrm{x}, mathrm{y}, mathrm{z} ) are in

JEE/Engineering Exams

Maths

Solution

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If x =∑^∞_n=0 a^n, y = ∑^∞_n=0 b^n, z = ∑^∞_n=0 c^n where a,b,c are in A.P. and |a|<1,|b|<1,|c|<1 then x,y,z are in

( x=frac{1}{1-a}, quad y=frac{1}{1-a} =frac{1}{1-e} )
( )
( a, 6, quad C quad A P )
( 1-9, quad 1-6, quad 1-C quad A P )
( frac{1}{1-a}, frac{1}{1-b}, frac{1}{1-c} HP)
( x , y , z ) (HP)

If ( x=sum_{n=0}^{infty} a^{n}, y=sum_{n=0}^{infty} b^{n}, z=sum_{n=0}^{infty} c^{n} ) where ( a, b, c ) are in A.P.and ( |mathrm{a}|<1,|mathrm{b}|<1,|mathrm{c}|<1 ) then ( mathrm{x}, mathrm{y}, mathrm{z} ) are in

If ( x=sum_{n=0}^{infty} a^{n}, y=sum_{n=0}^{infty} b^{n}, z=sum_{n=0}^{infty} c^{n} ) where ( a, b, c ) are in A.P.
and ( |mathrm{a}|<1,|mathrm{b}|<1,|mathrm{c}|<1 ) then ( mathrm{x}, mathrm{y}, mathrm{z} ) are in