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Question

Find the sum of n terms of the series 6+66+666+....

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Solution

Note that the given series is not a geometric series.
We need to find Sn=6+66+666+...to n terms
Sn=6(1+11+111+....to n terms )
=69(9+99+999+....to n terms) (Multiply and divide by 9)
=23[(101)+(1001)+(10001)+.... to n terms]
=23[(10+102+103+....n terms)n]
Thus, Sn=23[10(10n1)9n]

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