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Find the sum of the following series upto n terms. (1) 5 + 55What is the sum of the series 0.5 + 0.55 + 0.555 +. to n terms? 5 9 [nThe sum of n terms of the series 1 √ 3 + √ 5 + 1

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Find the sum of the following series upto n terms. (1) 5 + 55What is the sum of the series 0.5 + 0.55 + 0.555 +. to n terms? 5 9 [nThe sum of n terms of the series 1 √ 3 + √ 5 + 1

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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