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Let n be the number, then: 1/n - 1/3n = 1/6 Solve the subtraction on the left: 1/n - 1/3n = 3/3n - 1/3n = 2/3n But we know this is 1/6, thus: 2/3n = 1/6 ⇒ 3n = 12 ⇒ n = 4 Thus the number is 4.
3n+1=7 3*2+1=7
The Series has the formula 3n + 1/2(n - 1)(n - 2) = 3n + 1/2(n2 - 3n + 2) which simplifies to, 1/2(n2 +3n + 2)
3n + 4 = 7(- 4 from both sides)3n = 3(divide both sides by 3)n = 1