Use the approach in​ Gauss’s Problem to find

Christopher Stone

Christopher Stone

Answered question

2022-04-08

Use the approach in​ Gauss’s Problem to find the following sums of arithmetic sequences:
1) 1+2+3+4+.+999
2) 1+3+5+7+.+103
3) 4+9+14+19+.+504
4) 8881+872+863+854+.+8

Answer & Explanation

posciad48o

posciad48o

Beginner2022-04-09Added 15 answers

1) Using Gauss take the sum of terms from 1,2,,998 then add the sum to 999
1+2+3++499
998+997+996++500
999+999+999++999
Thus, sum is 999(499)+999=499500
2)1+3+5+7++103
1+3+5+7++51
103+101+99++53
104+104+104+104++104
Thus, sum is 26(104)=2704
3) 4+9+14+19++504
Take the sum of terms from 100 terms then add the 101 term to sum
4+9+14++249
499+494+489++254
503+503+503++503
Thus, sum is 50(503)+504=25654

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