Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Sequences & Series - Sigma notation.
Test Yourself 1.


 

For questions 1-6, write out the terms and then add them together. None of these six questions are standard series - so no short cut.

For the subsequent questions which are either arithmetic or geometric, identify the key variables and use the relevant summation relationship.

 

General interpretation. 1. Evaluate
Answer Sum = 36.		 2. Evaluate
Answer Sum = 91.

 

 3. Evaluate
AnswerSum = 77/60.		 4. Evaluate
Answer3+√2+√3.
  5. Evaluate
AnswerSum = 1707/440.		 6. Evaluate
AnswerSum = 5/12.
     
     
Use with arithmetic series. (i) Show that is an arithmetic series.

(ii) Hence evaluate this summation.

Answer(ii) Sum = 481.		 Find n if
Answern = 75.
     
     
Use with geometric series. 14. (i) Show that
represents a geometric series.

(ii) Evaluate the sum of the series.

 15. Evaluate

Express your answer as a surd with a rational denominator.

 
  16. Write as a series and then evaluate.
Answer. Sum = 70.