The value of 1 + 1 + frac{1}{4 times 3} + fra | vedclass

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(D) The given expression is $1 + 1 + \frac{1}{12} + \frac{1}{4 	imes 9} + \frac{1}{4 	imes 27}$.This simplifies to $2 + \frac{1}{12} + \frac{1}{36}

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none of these

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(D) The given expression is $1 + 1 + \frac{1}{12} + \frac{1}{4 	imes 9} + \frac{1}{4 	imes 27}$.This simplifies to $2 + \frac{1}{12} + \frac{1}{36} + \frac{1}{108}$.To add these fractions,find the least common multiple of $12, 36,$ and $108$,which is $108$.The expression becomes $2 + \frac{9}{108} + \frac{3}{108} + \frac{1}{108}$.Summing the fractions gives $2 + \frac{9 + 3 + 1}{108} = 2 + \frac{13}{108}$.Calculating the decimal value: $2 + 0.12037... = 2.12037...$.Rounding to four decimal places,we get $2.1204$.

The value of $1 + 1 + \frac{1}{4 \times 3} + \frac{1}{4 \times 3^{2}} + \frac{1}{4 \times 3^{3}}$ up to four places of decimals is

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