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GenaCL600 [577]
3 years ago
10

Use​ Gauss's approach to find the following sums​ (do not use​ formulas). 1+3+5+7+...999

Mathematics
1 answer:
muminat3 years ago
4 0
S=1+3+5+\cdots+995+997+999
S=999+997+995+\cdots+5+3+1
\implies 2S=(1+999)+(3+997)+(5+995)+\cdots+(995+5)+(997+3)+(999+1)

2S=\underbrace{1000+1000+\cdots+1000+1000}_{500\text{ times}}

(We are adding 500 instances of 1000 because that's how many odd numbers there are between 1 and 1000, inclusive.)

2S=500\times1000=500000
\implies S=250000
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