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find the sum of the following series up to n terms.5 + 55let s n denote the sum to n terms of the given series, then s n = 5 + 55 + 555 + ⋯ to n terms ⇒ s n = 5 [1 + 11 + 111 + ⋯ to n terms] ⇒ s n = 5 9 [9 + 99 + 999 + ⋯ to n terms] ⇒ s n = 5 9 [(10 − 1) + (10 2 − 1) + (10 3 − 1) + ⋯ (10 n − 1)] ⇒ s n = 5 9 [(10 + 10 2 + 10 3 + ⋯ 10 n) − n] ⇒ s n = 5 9 [10 × (10 n − 1
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