Question

Define what is a series?
a) adding all the numbers
b) subtracting all the numbers
c) multiplying all the numbers
d) dividing all the numbers

Answer 1

Hint: We need to know the concept of a series in order to solve this question. In a sequence, there is a set of infinite numbers which are labelled from 1 to infinity, but in a series, the sum of the quantities are taken one by one.

Complete step-by-step solution -
A series is defined to be the operation of adding the terms of an infinite set of quantities one after another, when a starting number is given.
It is interesting that even if we add an infinite number of quantities or numbers, the result of the sum can still be a finite quantity or number. For example, if the nth term is given by $\dfrac{1}{{{2}^{n}}}$, then the sum of such terms from n=1 to $\infty $is given by
\[\dfrac{1}{2}+\dfrac{1}{{{2}^{2}}}+\dfrac{1}{{{2}^{3}}}+...\text{ }upto\text{ }\infty =1\]
However, we note that the sum of the terms of a series may or may not give a finite number. In the options, the given options for a series are adding, subtracting, multiplying or dividing the numbers. Thus, as option (a) matches the definition of a series, the answer should be option (a).

Note: In this case, we just need to find the definition of series to answer the question. However, one should not get confused between the set of infinite numbers and a series as in a series, we have to take the sum of the numbers.