The sum S of first n natural numbers is given by the formula S= 2n(n+1)? .If S=231, find n

Answer:

Given

S = n(n+1)/2

Where n= 231

231 = n(n+1)/2

231 ✕ 2 = n2 + n

462 = n2 + n

Now n can be written as 22n – 21n

∴ n2 + 22n – 21n -463 = 0

Take common

n(n + 22) -21(n + 22) = 0

(n + 22)(n – 21) = 0

∴ n = -22 or n= +21

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