Find an explicit formula for a sequence of the form a1, a2, a3, ... with the initial terms given in Description below.

Question

1-(1/3), (1/2)-(1/4), (1/3)-(1/5), (1/4)-(1/6), (1/5)-(1/7), (1/6)-(1/8)

Answer 1

Find an explicit formula for a sequence of the form a1, a2, a3, ... with the initial terms given in Description below.

1-(1/3), (1/2)-(1/4), (1/3)-(1/5), (1/4)-(1/6), (1/5)-(1/7), (1/6)-(1/8)

a₁ = 1 - (1/3) = (1/1) - (1/3)

a₂ = (1/2) - (1/4)

a₃ = (1/3) - (1/5)

. . .

so,

a₁ = 1 - (1/3)

a_n = 1/n - (1/(n+2)) for n>1