Find the sum of series 9 + 99 + 999 + … to n terms.

Asked by Sakshi | 1 year ago |  53

##### Solution :-

9 + 99 + 999 + … to n terms.

The given terms can be written as

(10 – 1) + (100 – 1) + (1000 – 1) + … + n terms

(10 + 102 + 103 + … n terms) – n

By using the formula,

Sum of GP for n terms =

Where, a = 10, r = 10, n = n

=$$\dfrac{10 (10^n – 1)}{(10-1) }-n$$

= $$\dfrac{10}{9}$$(10n – 1) – n

=$$\dfrac{1}{9}$$ [10n+1 – 10 – 9n]

= $$\dfrac{1}{9}$$ [10n+1 – 9n – 10]

Answered by Sakshi | 1 year ago

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