Find the sum of series 0.5 + 0.55 + 0.555 + …. to n terms

Asked by Sakshi | 1 year ago |  70

##### Solution :-

0.5 + 0.55 + 0.555 + …. to n terms

Let us take 5 as a common term so we get,

5(0.1 + 0.11 + 0.111 + …n terms)

Now multiply and divide by 9 we get,

$$\dfrac{5}{9}$$ [0.9 + 0.99 + 0.999 + …+ to n terms]

$$\dfrac{5}{9}[\dfrac{9}{10} + \dfrac{9}{100} + \dfrac{9}{1000} + … + n terms]$$

This can be written as

$$\dfrac{5}{9}(\dfrac{n – 1}{9} )(1 – \dfrac{1}{10^n})$$

Answered by Sakshi | 1 year ago

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