SOLUTION: Please help me solve this equation: Use the Gauss technique to determine the sum for the following: (a) 1+2+3+...+250 (b) 5+10+15+...+305

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Question 350075: Please help me solve this equation: Use the Gauss technique to determine the sum for the following:
(a) 1+2+3+...+250
(b) 5+10+15+...+305
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
(a)S1= 1 +2 +3+...+ 250 |sum with the series reversed, 250 terms equals to
_____+250+249+248+..+1 | 251
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=250*251=62750=2*S1 => S1=31375

(b) 5+10+15+...+305=5*(1+2+3+...61)=5*S2,

S2=__1+2+3+...61
+S2=61+60+.....1
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=62*61=2*S2

=>S2=31*61=1830+61=1891 => 5*S2=5000+4000+450+5=9455(=310*313/2)