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Sigma notation
- Lesson: 1a8:56
- Lesson: 1b4:08
- Lesson: 28:59
- Lesson: 3a2:48
- Lesson: 3b4:19
- Lesson: 45:57
- Lesson: 57:13
- Lesson: 6a3:39
- Lesson: 6b3:14
- Lesson: 7a4:26
- Lesson: 7b3:06
Sigma notation
Don't you find it tiring when we express a series with many terms using numerous addition and/or subtraction signs? Don't you wish that we have something to symbolise this action? Well we have a solution, introducing the "Sigma Notation"! In this section, we will learn how to utilise the sigma notation to represent a series, as well as how to evaluate it.
Lessons
∑i=1n(an equation containing i)
∑ : "Sigma"; summation of ith term to nth term
i : index, a counter for the ith term
n : index of ending term
∑ : "Sigma"; summation of ith term to nth term
i : index, a counter for the ith term
n : index of ending term
- 1.Evaluate the following arithmetic series:
a)∑i=110ib)∑i=15−3(i+1) - 2.Write the following sum in sigma notation, then evaluate
7+9+11+13+...+205 - 3.Evaluate the following geometric series:
a)∑i=132(21)ib)∑i=120(−3)i+1 - 4.Write the following sum in sigma notation, then evaluate
−100+10−1+101−1001 - 5.Use sigma notation to express S10 for −5,10,−20,40,..., then evaluate
- 6.Evaluate the following infinite geometric series:
a)∑i=1∞3(−5)i−1b)∑i=1∞−27(−32)i - 7.Write the following sum in sigma notation, then evaluate
a)4+2+1+...b)1−2+4−8+...