SUMMATION FORMULA

When large number of data are concerned, then summation is needed quite often. To write a very large number, summation notation is useful.  The sequence [1,2,4,2..] whose value is the sum of the each number in the sequence is summation. In simple words, summation notation helps write a short form for addition of very large number of data. We use this symbol –

We use this symbol –  , called sigma to denote summation. When a sequence is needed to add from left to right, it could run intermediate result in a partial sum, running total or prefix sum.

The form in which the summation notation is used:

\[\large x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+……..x_{n}=\sum_{i-n}^{n}x_{i}\]

To make it clear, read what each notation in the summation formula stands for:

summationThis expression is read as “The sum of x sub i from i equals 1 to n”.

Solved Example

Question: Evaluate: $\sum_{x-0}^{4}x^{4}$ 

The expression can be written as:

$\sum_{x-0}^{4}x^{4}=\left(0\right)^{2}+\left(1\right)^{2}+\left(2\right)^{2}+\left(3\right)^{2}+\left(4\right)^{2}$

$=0+1+16+81+256=354$


Practise This Question

Identify the correct set of statements related to the movement of substances through vascular tissues.

I.   Xylem mainly translocates water, minerals salts and also organic solutes.

II.   Phloem mainly translocates a variety of organic solutes and also inorganic solutes.

III.  Xylem transports substances from roots to aerial parts of the plants.

IV. Phloem transports substances bidirectionally.