AP-GP

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A fun result. Its more suited for 11th students

A sequence is as follows:

1,2,3,4,5,10,20,40,80,160,...

i.e. the 1st 5 nos. in AP and then onwards a GP.

Prove that every natural number can be obtained as sums of distinct terms of this sequence.

#Mathematics #Algebra

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5 Answers

Devil ·2010-07-04 07:34:01

Any number can be written in the form of 2^a+2^b+....2^k, where a,b,....k are non-negative integers. Further every number is either of the form 5k, 5k+1, 5k+2, 5k+3 or 5k+4.

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Hari Shankar ·2010-07-05 01:26:54

@soumik-Yup. Juniors can still try

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Lokesh Verma ·2010-07-05 02:06:11

btw.. we can do this one even without 5?

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Dr.House ·2010-07-05 04:59:43

no one wants to even give a try?

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Lokesh Verma ·2010-07-06 12:05:21

even I am surprised it isnt so difficult either!

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Basic Integral Calculus Operators Symbols Matrix Cases

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AP-GP

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