Find the sum of series 0.6 + 0.66 + 0.666 + …. to n terms.

Asked by Sakshi | 1 year ago |  69

##### Solution :-

0.6 + 0.66 + 0.666 + …. to n terms.

Let us take 6 as a common term so we get,

6(0.1 + 0.11 + 0.111 + …n terms)

Now multiply and divide by 9 we get,

$$\dfrac{6}{9}$$ [0.9 + 0.99 + 0.999 + …+ n terms]

$$\dfrac{6}{9}$$ [$$\dfrac{9}{10}$$ + $$\dfrac{9}{100}$$ + $$\dfrac{9}{1000}$$ + …+ n terms]

This can be written as

$$\dfrac{6}{9}(1 – \dfrac{1}{10}) + (1 – \dfrac{1}{100}) + (1 -\dfrac{1}{1000}) + … + n terms]$$

$$\dfrac{6}{9}( \dfrac{n – 1}{9}) (1 – \dfrac{1}{10n})$$

Answered by Sakshi | 1 year ago

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