Sequences and Series Convergence

Determine if the series ∑(1/n) converges or diverges.

• Remains constant

• Diverges

• Converges

• Oscillates

Find the convergence of the series ∑(1/2^n).

• The series approaches infinity.

• The series oscillates.

• The series converges.

• The series diverges.

Investigate the convergence of the series ∑(n^2/2^n).

• The series ∑(n^2/2^n) diverges.

• The series ∑(n^2/2^n) converges.

• The series ∑(n^2/2^n) oscillates.

• The series ∑(n^2/2^n) approaches infinity.

Check the convergence of the series ∑(1/n^2).

• The series ∑(1/n^2) converges.

• The series ∑(1/n!) converges.

• The series ∑(1/n^3) converges.

• The series ∑(1/n) converges.

Examine the convergence of the series ∑(n!/n^n).

• The series tends to infinity

• The series diverges.

• The series oscillates

• The series converges

Determine if the series ∑(sin(n)/n) converges or diverges.

• The series ∑(sin(n)/n) diverges due to alternating signs.

• The series ∑(sin(n)/n) converges.

• The series ∑(sin(n)/n) converges to 0.

• The series ∑(sin(n)/n) converges to 1.

Find the convergence of the series ∑(1/(n*(n+1))).

• n^2

• 2

• 1

• 1/n

Investigate the convergence of the series ∑(n^3/3^n).

• The series ∑(n^3/3^n) converges.

• The series ∑(n^3/3^n) diverges.

• The series ∑(n^3/3^n) has a finite limit.

• The series ∑(n^3/3^n) oscillates.

Check the convergence of the series ∑(1/(n*log(n))).

• The series ∑(1/n) converges.

• The series ∑(1/(n^2)) converges.

• The series ∑(1/(n^2*log(n))) converges.

• The series ∑(1/(n*log(n))) diverges.

Examine the convergence of the series ∑(n^2/2^n).

• The series ∑(n^2/2^n) oscillates.

• The series ∑(n^2/2^n) converges.

• The series ∑(n^2/2^n) diverges.

• The series ∑(n^2/2^n) approaches infinity.