$k \left(1+2 \cdot 3^{-1}+3 \cdot 3^{-2}+4 \cdot 3^{-3}+\ldots \infty\right)=1$
$\text { Let } \quad s =1+\frac{2}{3}+\frac{3}{3^2}+\frac{4}{3^3}+\ldots \infty$
$\frac{s}{3}=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^2}+\ldots \infty$
$\frac{2 s}{3}=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^2}+\ldots \infty$
$\frac{2 s}{3}-\frac{1}{1-\frac{1}{3}}=\frac{3}{2}$
$s=\frac{9}{4}$
$k=\frac{4}{9}$
$P(x \geq 2)=1-P(x=0)-P(x=1)$
$=1-\frac{4}{9}\left(1+\frac{2}{3}\right)$
$=\frac{7}{27}$
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વિધાન $-1$ : $AB - BA$ એ હમેશા સામાન્ય શ્રેણિક છે .
વિધાન $-2$ : $AB -BA$ એ એકમ શ્રેણિક શક્ય નથી.