The infinite sum 5-13-55-132-555-133-5555-134- - equals

The correct option is E 5/13+55/13^2+555/13^3+5555/13^4+.....=5/9(9/13+99/13^2+999/13^3+.............) =5/9[10 1/13+100 1/13^2+1000 1/13^3..............] =5 ...

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The infinite ...

Question

The infinite sum $\frac{5}{13} + \frac{55}{13^{2}} + \frac{555}{13^{3}} + \frac{5555}{13^{4}} + . . . . .$ equals

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Solution

The correct option is C

$\frac{5}{13} + \frac{55}{13^{2}} + \frac{555}{13^{3}} + \frac{5555}{13^{4}} + . . . . . = \frac{5}{9} (\frac{9}{13} + \frac{99}{13^{2}} + \frac{999}{13^{3}} + . . . . . . . . . . . . .)$

$= \frac{5}{9} [\frac{10 - 1}{13} + \frac{100 - 1}{13^{2}} + \frac{1000 - 1}{13^{3}} . . . . . . . . . . . . . .]$

$= \frac{5}{9} [{{(\frac{10}{13})}^{1} + {(\frac{10}{13})}^{2} + {(\frac{10}{13})}^{3} + . . . . . . . . . .} - {(\frac{1}{13}) + {(\frac{1}{13})}^{2} + {(\frac{1}{13})}^{3} + . . . . . . . .}]$

Now solve this infinite GP to get $\frac{65}{36}$ Hence, option (c)

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The infinite sum 513+55132+555133+5555134+..... equals

The correct option is C 513+55132+555133+5555134+.....=59(913+99132+999133+.............) =59[10−113+100−1132+1000−1133..............] =59[{(1013)1+(1013)2+(1013)3+..........}−{(113)+(113)2+(113)3+........}] Now solve this infinite GP to get 6536 Hence, option (c)

The infinite sum $\frac{5}{13} + \frac{55}{13^{2}} + \frac{555}{13^{3}} + \frac{5555}{13^{4}} + . . . . .$ equals