Page 112 - ADVANCED MATH F.5

Form Five Form Five

Summation of series using partial fractions

Teaching steps
1. Guide students in groups to discuss the concept of telescopic
series. Ask students to explore the behavior of a telescopic
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series through additional resources, such as online tutorials or
reference books.
2. Use Examples 5.71 and 5.72 in the Student’s Book, to guide
students to find the sum of the series using partial fractions.

3. Direct students to attempt Exercise 5.13, in the Student’s Book.
Advise students to submit their work. Check the correctness of
their answers, and provide them constructive feedback.

Answers to Exercise 5.13

1 2 1 1 1 2
1. − + ; s = s = 0 3. 2 − − ; s = 2
n n + 1 n + 2 ∞ ∞ 4 n + 1 n + 2 ∞

1 1 1 1 1 n + 3
;
4. 2n − 1 2n + − 1 2 − 2n + 1 5. 2 + (2n + 12n + )( ) 3

1 1 1 11
6. − 7. −
n n + 2 4(2k − 1) 4(2k − ( 42k + 3)) 3

3 2n + 1
9. 8 − (2n + 2 )(2n + ) 6

1 n + 2 11 1  1 1 1 
10. (a) 6 − (n + 3 )(n + ) 4 (b) 18 3 n +  −  1 n + + 2 + n + 3  

1 1
(c) 9 − ( 9 n + ) 1

106
Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 106