2.mathop {357}limits^{ bullet ,, bullet ,, bu | vedclass

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Question

(c) Given that $2.\mathop {357}\limits^{.\,\,\,.\,\,\,.} = 2.357357357357......$

$ = 2 + 0.\mathop {357}\limits^{} + 0.000357 + 0.000000357 + .....

Vedclass · Accepted Answer

$\frac{{2355}}{{999}}$

Vedclass · Answer

(c) Given that $2.\mathop {357}\limits^{.\,\,\,.\,\,\,.} = 2.357357357357......$

$ = 2 + 0.\mathop {357}\limits^{} + 0.000357 + 0.000000357 + .......\infty $
 

$ = 2 + \frac{{357}}{{{{10}^3}}} + \frac{{357}}{{{{10}^6}}} + \frac{{357}}{{{{10}^9}}} + .......$

$	herefore $ ${S_\infty } = 2 + \frac{{\frac{{357}}{{{{10}^3}}}}}{{1 - \frac{1}{{{{10}^3}}}}} = 2 + \frac{{357}}{{{{10}^3}}} 	imes \frac{{{{10}^3}}}{{999}} = \frac{{2355}}{{999}}$.

$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $

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