Converging series · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Telescoping series and convergence — objective 1

Maths4U Original · Short practice

For \(a=11,\ n=14\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{3}{r(r+1)}\).

Find \(\displaystyle S_{n}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Telescoping series and convergence — objective 1

Maths4U Original · Short practice

For \(a=12,\ n=15\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{4}{r(r+1)}\).

Find \(\displaystyle S_{n}\).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Telescoping series and convergence — objective 2

Maths4U Original · Short practice

For \(a=12,\ n=15\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{4}{r(r+1)}\).

Find the sum from \(\displaystyle r=a\) to infinity.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Telescoping series and convergence — objective 2

Maths4U Original · Short practice

For \(a=13,\ n=16\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{2}{r(r+1)}\).

Find the sum from \(\displaystyle r=a\) to infinity.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Telescoping series and convergence — objective 3

Maths4U Original · Short practice

For \(a=13,\ n=16\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{2}{r(r+1)}\).

Find the positive remainder after n terms.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Telescoping series and convergence — objective 3

Maths4U Original · Short practice

For \(a=14,\ n=17\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{3}{r(r+1)}\).

Find the positive remainder after n terms.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Telescoping series and convergence — objective 4

Maths4U Original · Short practice

For \(a=14,\ n=17\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{3}{r(r+1)}\).

Find the first term of the series.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Telescoping series and convergence — objective 4

Maths4U Original · Short practice

For \(a=15,\ n=18\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{4}{r(r+1)}\).

Find the first term of the series.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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