Given series 1112141 habituated to write data given in the question at the beginning of an answer thanks to indian methods of education so what i notice in this pattern is that all of the odd numbers have been denoted by 1 and the even numbers have been denoted using successive powers of 2. Mathdisplaystylefrac 1 2times frac 2 3times frac 3 4times frac 4 5 frac45frac 1 5 math this is also an example of a telescoping product where the denominator of one factor cancels the nominator of the subsequent factor. The fact that you are asking this question when you have learned about infinite geometric progressions is good because it shows you are interested in math and thinking about what you are doing and not just learning how to pass the next test
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