The correct option is D Given that 2.⋯357 = 2.3573573573 57... = 2 + 0.357 + 0.000357 + 0.000000357 + ....∞ = 2 + 357/10^3 + 357/10^6 + 357/10^9 + ... ∴ S_∞ = ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

2.357=

Question

$2. \dots 357$ =

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None of these

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Solution

The correct option is C

Given that $2. \dots 357$ = 2.3573573573 57...
$= 2 + 0.357 + 0.000357 + 0.000000357 + . . . . \infty$
$= 2 + \frac{357}{10^{3}} + \frac{357}{10^{6}} + \frac{357}{10^{9}} + . . .$
$∴ S_{\infty} = 2 + \frac{\frac{357}{10^{3}}}{1 - \frac{1}{10^{3}}} = 2 + \frac{357}{10^{3}} \times \frac{10^{3}}{999} = \frac{2355}{999} .$

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Similar questions

Q. The value of

2. ¯ ¯¯¯¯¯¯ ¯ 357

The fractional value of $2.357$ is

The rational number which equals the number

2. ¯ ¯¯¯¯¯¯ ¯ 357

with recurring decimal is

The rational number which is equal to the number 2.357 with recurring decimal is

Q. The fractional value of 2.357 is
(a) 2355/1001
(b) 2379/997
(c) 2355/999
(d) none of these

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2.⋯357=

The correct option is C Given that 2.⋯357 = 2.3573573573 57... =2+0.357+0.000357+0.000000357+....∞ =2+357103+357106+357109+... ∴S∞=2+3571031−1103=2+357103×103999=2355999.

$2. \dots 357$ =