the sum of the first n natural number is given by the relation as browser 1.2 and Bracket and + 1 find the value of n is as barabar 153
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The sum ‘S’ of the first ‘n’ natural numbers is given by S = n (n + 1)/2 . Find ‘n’, if the sum (S) is 276.
Sol. S = n (n + 1)/2∴ 276 = n (n + 1)/2∴ 276 × 2 = n(n+1)∴ 552 = n2 + n∴ n2 + n – 552 = 0∴ n2 + 24n – 23n – 552 = 0∴ n (n + 24) (n – 23) = 0∴ n + 24 = 0 or n – 23 = 0∴ n = – 24 or n = 23∵ Number of terms cannot be negative,
∴ n = 23
Sol. S = n (n + 1)/2∴ 276 = n (n + 1)/2∴ 276 × 2 = n(n+1)∴ 552 = n2 + n∴ n2 + n – 552 = 0∴ n2 + 24n – 23n – 552 = 0∴ n (n + 24) (n – 23) = 0∴ n + 24 = 0 or n – 23 = 0∴ n = – 24 or n = 23∵ Number of terms cannot be negative,
∴ n = 23
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