SOLUTION: Use Gauss's approach to find the following sums(do not use formulas). a. 1+2+3+4+...+99 b. 1+3+5+7+...+97 a. The sum of the sequence is? b. the sum of the sequence is?

Algebra ->  Signed-numbers -> SOLUTION: Use Gauss's approach to find the following sums(do not use formulas). a. 1+2+3+4+...+99 b. 1+3+5+7+...+97 a. The sum of the sequence is? b. the sum of the sequence is?      Log On


   

Question 764843: Use Gauss's approach to find the following sums(do not use formulas).
a. 1+2+3+4+...+99
b. 1+3+5+7+...+97
a. The sum of the sequence is?
b. the sum of the sequence is?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a. 1+2+3+4+...+99
1%2B99+=+100
99%2F2=49.5
sum=100%2A49.5=+4950
b. 1+3+5+7+...+97
first find the sum 1+2+3+4+...+97
1%2B97+=+98
98%2F2=49
sum=98%2A49=+4802
since you have only odd numbers, it will be half of 4802 which is 2401
so, the sum of 1+3+5+7+...+97 is 2401