Question

( a=sum_{n=0}^{infty} x^{n}=1+x+x^{2} )
Sum of infinite ( epsilon_{1} cdot p=frac{a}{1-r} )
ther ( a=1 quad ) and ( r=x )
( a=frac{1}{1-x} quad ) similally ( quad b=frac{1}{1-y} )
and ( c=frac{1}{1-x y} )
( left(frac{-1}{a}+1right)=x quad ) and ( quadleft(frac{-1}{b}+1right)=x y )
and ( left(frac{-1}{c}+1right)=x y )
( therefore quadleft(1-frac{1}{a}right)left(1-frac{1}{b}right)=left(1-frac{1}{c}right) )
( x-frac{1}{a}-frac{1}{b}+frac{1}{a b}=x-frac{1}{c} )
( b+a-1=-frac{a b}{c} )
( Rightarrow a b+b c=a b+c )
; corred ans. is ( (C) )

# If a = Ex”,b={y',c=Ś(x" where 11.101<1; then- n=0 n=0 n=0 (A) abc = a + b + c (C) ac + bc = ab + c (B) ab + bc = ac + b (D) ab + ac = bc + a

Solution