smadrid1293 smadrid1293

04-09-2017
Mathematics

contestada

What is the sum of the sequence 1+3+5+7+...+99
Use Gauss's approach to find the following sum.

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mathmate mathmate

05-09-2017

Gauss's approach is to add the same sequence in reverse order, namely

S=1+3+5+7+......+95+97+99
S=99+97+95+......+7+5+3+1
---------------------------------------
2S=(1+99)+(3+97)+(5+95)+......(95+5)+(97+3)+(99+1)=50*100=5000
=> sum = (2S)/2 = 5000/2=2500.

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