If a = Ex”,b={y',c=Ś(x" where 11.10...
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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

JEE/Engineering Exams
Maths
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( 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) )
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