Sequence Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Write the first four terms of

b_n = (-1)^n \cdot \frac{1}{n}

1
$b_1 = -1$ , $b_2 = \frac{1}{2}$ , $b_3 = -\frac{1}{3}$ , $b_4 = \frac{1}{4}$ .

Answer

-1,\; \frac{1}{2},\; -\frac{1}{3},\; \frac{1}{4}

The factor

(-1)^n

alternates the sign. Despite the oscillation, magnitudes

1/n

shrink to 0, so this alternating sequence converges to 0.

About Sequence

An ordered list of numbers generated by a rule, where each number has a specific position (first, second, third, ...).

Write the first five terms of the sequence [formula] for [formula]

Determine whether the sequence [formula] converges or diverges. If it converges, find the limit.

Determine whether [formula] converges or diverges.