Complete the following series-
1 , 11, 21 , 1211 , 111221 .......
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Solution: If you interpret the elements of the sequence as numerical quantities, there seems to be no obvious pattern. But who said that they are numbers? If you look at the relationship between an element and its predecessor and focus on "symbolic" content, we see a pattern. Each element "describes" the previous one. For example, the third element is 2 1, which can be described as "one 2 and one 1," i.e., 1 2 1 1, which is the fourth element. This can be described as "one 1, one 2 and two Is," i.e., 1 1 1 22 1. S o the next member is 3 1 22 1 1 ("three 1 s, two 2s and one 1 ").