Intro to Summation (Σ) and Product (Π) Notation
Read this topicExplanations 6
- A sum is the result of adding a sequence of values. For example, 1+4+9+161+4+9+161+4+9+16 is the sum of the first four squares. We can write this sum compactly using sigma notat…
By Alexander Wei, Ray Li, Anusha Rahman
- Summations A summation, or a sum for short, is the sum of a list of numbers. For example, the sum of 1,2,3,41,2,3,41,2,3,4 is 1+2+3+4=101+2+3+4=101+2+3+4=10. We can write these …
By Daniel Liu, Brian Sterr, Vinjai Vale, Moor Xu, Expii Team, Anusha Rahman
- Sums A summation is simply a shorthand for summing terms given by a formula together. These "sums" are things like 2+4+6+82+4+6+82+4+6+8 or 1+12+14+⋯1 + \frac 12 + \frac 14 + \c…
By Eric Zhang, Expii Team
- Summation notation Sigma notation is a shorthand form used to denote a sum of many values. A summation is denoted by the capital Greek letter ∑\sum∑ (sigma): ∑i=1nai=a1+a2+a3+..…
By Catherine Yeo, amaterasu, Alex Federspiel
- (Video) Sigma Notation by Eddie Woo Here's a video by Eddie Woo where he explains what sigma notation is and how you use it. To recap, there's three ways to define a series or s…
By Alex Federspiel, Anusha Rahman
- Summation Notation Summation notation helps us simplify how we write out sequences and series. Sigma notation or summation notation helps us quickly and efficiently write out th…
By Anusha Rahman
Problems 14
- ∏i=15i=\begin{align} \prod_{i=1}^5 i &=\end{align}i=1∏5i=
- ∏i=13(∑j=1ij)=\begin{align} \prod_{i=1}^3 \left(\sum_{j=1}^i j\right) = \end{align}i=1∏3(j=1∑ij)=
- 11−(∑i=1512i)=\begin{align} \frac{1}{1 - \left(\sum_{i=1}^5 \frac{1}{2^i}\right)} = \end{align}1−(∑i=152i1)1=
- ∑m=13(∑n=23(−1)m+nmn)=\begin{align} \sum_{m=1}^3 \left(\sum_{n=2}^3 (-1)^{m+n} m^n\right) = \end{align}m=1∑3(n=2∑3(−1)m+nmn)=
- ∑i=37(3i−2)=\begin{align} \sum_{i=3}^7 (3i-2) &= \end{align}i=3∑7(3i−2)=
- ∏i=1274(−1)=\begin{align} \prod_{i=1}^{274} (-1) &= \end{align}i=1∏274(−1)=
- Define a function f:R→Rf:\mathbb{R} \to \mathbb{R}f:R→R as follows: f(x)={1if x is divisible by 2−1if x is divisible by 3, but not by 20otherwisef(x) = \begin{cases} 1 &\text{if…
- Let xxx be a real number and consider the sequence defined by an=4xna_n = 4xnan=4xn. In terms of xxx, what is the value of the following expression? ∑n=15an\sum_{n=1}^5 a_nn=1∑…
- Compute ∏k=22016k−1k.\prod_{k=2}^{2016} \frac{k-1}{k}.k=2∏2016kk−1.
- Let ana_nan be a sequence and kkk be a natural number; also assume that ∑n=1kan=5\sum_{n=1}^k a_n = 5n=1∑kan=5 If we define a new sequence by bn=3anb_n = 3a_nbn=3an, find t…
- Assume that we have a sequence such that, for n≥2n \ge 2n≥2, an=an−1−2an−2a_n = a_{n-1} - 2a_{n-2}an=an−1−2an−2. Also assume that a0a_0a0 and a1a_1a1 are given. In terms of…
- ∑i=14i(i−1)=\sum_{i=1}^4 i^{(i-1)} =i=1∑4i(i−1)=
- Which of the following is equal to: ∑i=131(x+1)i\sum_{i=1}^3 \frac{1}{(x+1)^i}i=1∑3(x+1)i1
- What is the value of ∑n=010an\sum\limits_{n=0}^{10} a_nn=0∑10an?