Find the sum of the sequence ^@5, 55, 555, 5555,^@ toLet S = 0.5 + 0.55 + 0.555 + upto 20 terms = 5 10 + 55 100 + 555 10 3 + + upto 20 terms = 5 [1 10 + 11 100 + 111 10 3 + + upto 20 terms] Multiplying and dividing the RHS by 9, we get S = 5 9 [((1 − 1 10) + (1 − (1 10) 2) + (1 − (1 10) 3)) +.. upto 20 terms] = 5 9 [20 − 1 10 (1 − (1 10) 20) 1 − 1 10] = 5 9 [179 9 + 1 9 (1
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