The value of the expression - 2-1-3 - - 2-3-5 - - 2-5-7 - - 2-997-999 - is equal to

The correct option is A 1001/3 Given expression =5/3×7/5×9/7×......999/997×1001/999 =1001/3 (Since the others cancel out) ...

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Standard X

Mathematics

Addition Theorem of Probability for 2 Events

The value of ...

Question

The value of the expression
$[2 - \frac{1}{3}] [2 - \frac{3}{5}] [2 - \frac{5}{7}]$ ... $[2 - \frac{997}{999}]$ is equal to

\frac{1001}{3}

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\frac{1}{999}

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\frac{1}{3}

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Solution

The correct option is A $\frac{1001}{3}$
Given expression

$= \frac{5}{3} \times \frac{7}{5} \times \frac{9}{7} \times . . . . . . \frac{999}{997} \times \frac{1001}{999}$

$= \frac{1001}{3}$ (Since the others cancel out)

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Similar questions

$12 \times (2 - \frac{1}{3}) \times (2 - \frac{3}{5}) \times (2 - \frac{5}{7}) \times (2 - \frac{7}{9}) \times (2 - \frac{9}{11}) \dots \dots \dots (2 - \frac{997}{999}) \times (\frac{1}{2002})$ = ?

Q. What is the value of

999 \frac{1}{7} + 999 \frac{2}{7} + 999 \frac{3}{7} + 999 \frac{4}{7} + 999 \frac{5}{7} + 999 \frac{6}{7}

when simplified?

999 \frac{1}{7} + 999 \frac{2}{7} + 999 \frac{3}{7} + 999 \frac{4}{7} + 999 \frac{5}{7} + 999 \frac{6}{7} =

Q. The value of

1000 [\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + . . . + \frac{1}{999 \times 1000}]

is equal to

Q. The value of

1000 [\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + . . . . . \frac{1}{999 \times 1000}]

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The value of the expression [2−13][2−35][2−57]...[2−997999] is equal to

The correct option is A 10013Given expression=53×75×97×......999997×1001999=10013 (Since the others cancel out)

The value of the expression
$[2 - \frac{1}{3}] [2 - \frac{3}{5}] [2 - \frac{5}{7}]$ ... $[2 - \frac{997}{999}]$ is equal to

The correct option is A $\frac{1001}{3}$
Given expression

$= \frac{5}{3} \times \frac{7}{5} \times \frac{9}{7} \times . . . . . . \frac{999}{997} \times \frac{1001}{999}$

$= \frac{1001}{3}$ (Since the others cancel out)