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What is 1+2+4+6+8+10+................1000?

Try to break it up.

 Oct 17, 2016
 #1
avatar+118653 
0

What is 1+2+4+6+8+10+................1000?

It is not a proper sequence but it looks like

1+          2+4+6+8+10+................1000?

1+ an AP with a=2, d=2 and Last term=1000

 

\(Sum=1\;\;\;+\;\;\;\frac{n}{2}(a+L)\\ n=?\;\;\;a=2\;\;\;L=1000 \quad find \;\;n\\~\\ \quad t_n=a+(n-1)d\\ \quad1000=2+(n-1)*2\\ \quad1000=2n\\ \quad n=500\\~\\ Sum=1\;\;\;+\;\;\;\frac{500}{2}(2+1000)\\ Sum=1\;\;\;+\;\;\;250*(1002)\\\)

 

Sum = 1+250*1002 = 250501

 Oct 17, 2016
 #2
avatar+118653 
0

laugh       Welcome to the Web2.0calc  forum ant101      laugh

 Oct 17, 2016

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