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Question

If 5+55+555+to n terms=581(10n+1+x+yn), then the value of yx is

A
1
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B
19
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C
1
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D
19
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Solution

The correct option is A 1
Let Sn denote the sum to n terms of the given series, then
Sn=5+55+555+to n termsSn=5[1+11+111+to n terms]Sn=59[9+99+999+to n terms]Sn=59[(101)+(1021)+(1031)+(10n1)]Sn=59[(10+102+103+10n)n]Sn=59[10×(10n1)101n]Sn=59[109×(10n1)n]Sn=581[10n+1109n]x=10,y=9yx=1

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