Let x _{1}, x _{2}, x _{3}, ldots ., x _{20} | vedclass

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Question

$\sum x _{0}^{1}=\frac{3\left(1-\left(\frac{1}{2}\right)\right)^{20}}{1 \frac{-1}{2}}=6\left(1-\frac{1}{2^{20}}\right)$

$=\sum_{ i =1}^{20}\left( x

Vedclass · Accepted Answer

$142$

Vedclass · Answer

$\sum x _{0}^{1}=\frac{3\left(1-\left(\frac{1}{2}ight)ight)^{20}}{1 \frac{-1}{2}}=6\left(1-\frac{1}{2^{20}}ight)$

$=\sum_{ i =1}^{20}\left( x _{ i - i }ight)^{2}$

$=\sum_{ i =1}^{20}\left( x _{ i }ight)^{2}+( i )^{2}-2 x _{ i } i$

Now $=\sum_{i=1}^{20}\left(x_{i}ight)^{2}=\frac{9\left(1-\left(\frac{1}{4}ight)ight)^{20}}{1-\frac{1}{4}}=12\left(1-\frac{1}{2^{40}}ight)$

$\sum_{i=1}^{20} i^{2}=\frac{1}{6} 	imes 20 	imes 21 	imes 41=2870$

$\sum_{ i =1}^{20} x _{ i } i = s =3+2.3 \frac{1}{2}+3.3 \frac{1}{2^{2}}+4.3 \frac{1}{2^{3}}+\ldots \ldots AGP$

$=6\left(2-\frac{22}{2^{20}}ight)$

$\overline{ x }=\frac{12-\frac{12}{2^{40}}+2870-12\left(2-\frac{22}{2^{20}}ight)}{20}$

$\overline{ x }=\frac{2858}{20}+\left(\frac{-12}{2^{40}}+\frac{22}{2^{20}}ight) 	imes \frac{1}{20}$

${[\overline{ x }]=142 }$

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