Homework SourseAssessment 11 A b Use the approach in Gausss Problem to find
Assessment 1.1 A b. Use the approach in Gauss\'s Problem to find the following sums of arithmetic sequences (do not use formulas): b. 1+3+5+7...+1001
Solution
1 +3 +5 +7+.....+999+1001
there are total 501 terms so to make it Even numer of terms let\'s skip last term 1001
now we are left with 1 +3 +5 +7+.....+999...(i)
write this in reverse order
999 +997 +....+1...(ii)
take sum of both
sum 1000 +1000 +1000 +...+1000
There are 500 of these sums. the total is 500 * 1000 = 500000, since this sum is twice the sum of the numbers 1 +3 +5 +7 +....1003, we have
sum 1 +3 +5 +7+.....+999 = 500000/2 = 250000
Now add 1001 that we skipped before
hence 1 +3 +5 +7+.....+999+1001=250000+1001=251001
So final answer is 251001
