Some difficult S.2 maths (10分)

a.1. x = 1 / (n + 1)

x(n + 1) = 1

xn + x = 1

xn = 1 – x

n = (1 - x) / x

So, y = n / (n - 1)

y = [(1 - x) / x] / [(1 - x) / x - 1]

y = [(1 - x) / x] / [(1 – x - x) / x]

y = (1 - x) / (1 – 2x)

b. y = n / (n - 1)

y(n - 1) = n

yn – n = 1

n(y - 1) = 1

n = 1 / (y - 1)

So, x = 1 / (n + 1)

x = 1 / [1 / (y - 1) + 1]

x = 1 / [(1 + y - 1) / (y - 1)]

x = (y - 1) / y