If the common ratio of an infinite G.P be less than 1/2, show that each term will be greater than the sum of all the terms that follows it.

Dear student,

Let us represent the G.P. as :

a, ar2, ar3, ar4, ar5, ..................Where, a = First term , r = common ratioAccording to the question,r < 12Sum of infinite G.P. = a1 - rThe denominator (1-r) < (-12)Now, let us take ar² as the first term, thenSum = ar²1 - r, since  (1-r) < (-12)Sum < a Similarly if we take the first term as ar3, then sum <ar²And so on 

Hence, we can say that each term is greater then sum of all the terms that follows it.


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when r is less than 1 then Sn=a+ (1-r raise to n)/1-r
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