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Taking 9 in common we get . 9(1 + 11 + 111 + ....n) Now Multiply and Divide by 9 we get, Now first term is in GP. 10, 100, 1000…to n terms. ∴ Common Ratio = r = \(\frac{100}{10}\) = 10. ∴ Sum of GP for n terms = \(\frac{a(r^n - 1)}{r-1}\) ..... (1) ⇒ a = 10, r = 10, n = n. ∴ Substituting the above values in (1) we get
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