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Question

8 + 88 + 888 + .............n terms = ____


A

8081(10n1)8n9

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B

1081(10n1)

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C

8081(10n1)+8n9

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D

8081(10n1)n9

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Solution

The correct option is A

8081(10n1)8n9


S=8+88+888+..... =8[1+11+111....] =89[9+99+999+......] =89[(101)+(1021)+(1031)+.....] =89[(10+102+103+......)(1+1+1+......)] =89[10×10n1101n]
=89[10×10n19n]
=8081(10n1)8n9


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