Mathematics, 19.12.2020 21:40 TheGingerDevl7762
WILL GIVE BRAINLIEST! Find the sum of the positive even integers up and including 50.
Answers: 2
![Well, we\ can\ solve\ the\ question\ by\ following\ some\ simple\ steps.\\Lets\ first\ set\ up\ an\ equation\ representing\ the\ Sum\ as\ S.\\Hence\ let\ this\ be\ E_1,\\S=1+2+3....50\ \\Now,\\By\ focusing\ on\ the\ RHS\ of\ the\ equation,\\1+2+3...50=50+49+48....1 [Commutative\ Property\ Of\ Addition]\\Hence\ let\ this\ be\ E_2,\\S=50+49+48....1\\By\ adding\ E_1\ and\ E_2,\\S=1+2+3...50\\S=50+49+48...1\\We\ get,\\2S=51+51+51.....51\\](/tpl/images/1002/8231/eafdd.png)
![Now,\\As\ we\ know\ that,\\The\ sum\ of\ all\ odd\ positive\ integers\ to\ a\ number\ n, where\ x\ is\ the\ number\ of\\ integers\ between\ 1\ and\ n, is\ given\ by\ the\ formula: \\S_{(all\ odds\ till\ n)}=x^2\\Now,\\x=\frac{(n+1)}{2}\\Hence,\\S_O= [\frac{(n+1)}{2}]^2\\Hence,\\As\ n\ can\ only\ be\ odd,\ n=50-1=49\\Hence,\\S_O=[\frac{(49+1)}{2}]^2\\S_O=25^2\\S_O=625\\If\ Sum\ of\ all\ even\ integers\ would\ be\ S_E,,\\As\ S_O+S_E=S\\Hence,\\625+S_E=1275\\Hence,\\S_E=1275-625\\S_E=650](/tpl/images/1002/8231/04046.png)
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WILL GIVE BRAINLIEST! Find the sum of the positive even integers up and including 50....
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