Brunei Math Club

The summation symbol is simply a shorthand notation for a sum of many numbers or variables. Let's see some examples first. Example . The sum  $$1+2+3+\cdots +10$$ can be written as $$\sum _{i=1}^{10}i.$$ That is, $$\sum _{i=1}^{10}i=1+2+3+\cdots +10.$$ Here, the symbol $\sum$ is called the summation symbol, $i$ is the index . The above expression means we take the sum of $i$ where the value of $i$ varies from 1 to 10. □ Remark . The letter $\sum$ (pronounced sigma ) is an uppercase letter from the Greek alphabet that corresponds to the letter S in the English alphabet. Why S? Because $\mathrm{\Sigma }$ stands for S ummation. □ Let's see some more examples. Example .   $$\sum _{k=1}^{10}{k}^2=1^2+2^2+3^2+\cdots +{10}^2.$$ We can use any letter for the index ($i$, $k$, etc.). □ Example .  $$\sum _{k=1}^{100}1=1+1+\cdots +1\text{(adding 1 for100 times)}$$ The index needs not appear in the ``body'' of the summation symbol. In this case, ...