Let, $F_1, F_2, F_4, F_8 \ldots \ldots$ be the forces of gravitation due masses ' $m$ ' at $x=1,2,4,8 \ldots$ respectively.
$\Rightarrow F_1=\frac{G m^2}{1^2}$
$F_2=\frac{G m^2}{2^2}$
$F_4=\frac{G m^2}{4^2}$
$F_8 =\frac{G m^2}{8^2}$
$F_1+F_2+F_4+F_8 \ldots=G m^2\left(\frac{1}{1}+\frac{1}{4}+\frac{1}{16}+\frac{1}{64} \ldots\right)$
infinite $G.P$. with common ratio $=\frac{1}{4}$
For an infinite $G.P$, sum $=\left(\frac{a}{1-r}\right)$
$a$ is the first term
$r$ is the common ratio
$\Rightarrow \text { Sum }=\frac{1}{1-\frac{1}{4}}=\left(\frac{4}{3}\right)$
$\Rightarrow F_1+F_2+F_4+F_8 \ldots \ldots=\frac{4}{3} G m^2$
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($A$) The error in the measurement of $r$ is $10 \%$
($B$) The error in the measurement of $T$ is $3.57 \%$
($C$) The error in the measurement of $T$ is $2 \%$
($D$) The error in the determined value of $g$ is $11 \%$
