Question

Write the first five terms of the following sequence and obtain the corresponding series:

`a_1 = -1, a_n = (a_(n-1))/n , n >= 2`

Answer 1

a₁ = −1, a_n = `"a"_("n"-1)/"n"`,

By placing 2, 3, 4, 5 in n,

a₂ = `"a"_1/2 = (-1)/2`,

a₃ = `"a"_2/3 = ((-1)/2)/3 = (-1)/6`

a₄ = `"a"_3/4 = ((-1)/6)/4 = (-1)/24`

a₅ = `"a"_4/5 = ((-1)/24)/5 = (-1)/120`

Hence, the first five terms of the given sequence are `−1 + (-1)/2 + (-1)/6 + (-1)/24 + (-1)/120`

The corresponding series is = `(−1) + ((-1)/2) + ((-1)/6) + ((-1)/24) + ((-1)/120) +...`