Find the sum of the series 5 + 55 + 555 + … to n terms.

Asked by Sakshi | 1 year ago |  73

##### Solution :-

5 + 55 + 555 + … to n terms.

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

5 [1 + 11 + 111 + … n terms]

Now multiply and divide by 9 we get,

$$\dfrac{5}{9}$$ [9 + 99 + 999 + … n terms]

$$\dfrac{5}{9}$$[(10 – 1) + (102 – 1) + (103 – 1) + … n terms]

$$\dfrac{5}{9}$$[(10 + 102 + 103 + … n terms) – n]

So the G.P is

$$\dfrac{5}{9}$$[(10 + 102 + 103 + … n terms) – n]

Where, a = 10, r = $$\dfrac{10^2}{10}$$ = 10, n = n Answered by Sakshi | 1 year ago

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