Find the sum of series 7 + 77 + 777 + … to n terms.

Asked by Sakshi | 1 year ago |  82

##### Solution :-

7 + 77 + 777 + … to n terms.

Let us take 7 as a common term so we get,

7 [1 + 11 + 111 + … to n terms]

Now multiply and divide by 9 we get,

$$\dfrac{7}{9}$$ [9 + 99 + 999 + … n terms]

$$\dfrac{7}{9}$$[(10 – 1) + (102 – 1) + (103 – 1) + … + (10n – 1)]

$$\dfrac{7}{9}$$ [(10 + 102 + 103 + … +10n)] –$$\dfrac{7}{9}$$ [(1 + 1 + 1 + … to n terms)]

So the terms are in G.P

Where, a = 10, r = $$\dfrac{10^2}{10}$$ = 10, n = n

By using the formula,

Sum of GP for n terms =

$$\dfrac{7}{9}$$ [$$\dfrac{10}{9}$$ (10n – 1) – n]

$$\dfrac{7}{81}$$[10 (10n – 1) – n]

$$\dfrac{7}{81}$$(10n+1 – 9n – 10)

Answered by Sakshi | 1 year ago

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