Problem:
What is the value in simplest form of the following expression?
1​+1+3​+1+3+5​+1+3+5+7​
Answer Choices:
A. 5
B. 4+7​+10​
C. 10
D. 15
E. 4+33​+25​+7​
Solution:
We have
1​+1+3​+1+3+5​+1+3+5+7​=1​+4​+9​+16​=1+2+3+4=(C)10​
Note: This comes from the fact that the sum of the first n odds is n2.
The problems on this page are the property of the MAA's American Mathematics Competitions