End-of-chapter review exercise 3 · 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

Finite power sums — objective 1

Maths4U Original · Short practice

Let \(n=14,\ S=\sum_{r=1}^n(5r^2+12r+1)\). Use the standard summation identities.

Find the sum of r from 1 to 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

Finite power sums — objective 1

Maths4U Original · Short practice

Let \(n=15,\ S=\sum_{r=1}^n(2r^2+13r+1)\). Use the standard summation identities.

Find the sum of r from 1 to n.

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

Method

Finite power sums — objective 2

Maths4U Original · Short practice

Let \(n=15,\ S=\sum_{r=1}^n(2r^2+13r+1)\). Use the standard summation identities.

Find the sum of r squared from 1 to 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

Finite power sums — objective 2

Maths4U Original · Short practice

Let \(n=16,\ S=\sum_{r=1}^n(3r^2+14r+1)\). Use the standard summation identities.

Find the sum of r squared from 1 to n.

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 \(a=14,\ n=17\), 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.

Fresh review variant

Telescoping series and convergence — objective 3

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 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 \(a=15,\ n=18\), 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.

Fresh review variant

Telescoping series and convergence — objective 4

Maths4U Original · Short practice

For \(a=16,\ n=19\), consider \(\displaystyle S_n=\sum_{r=a}^{a+n-1}\frac{2}{r(r+1)}\).

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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