Question

What is the sum of the first 100 positive odd numbers?

Answer 1

`a_1=1;\ a_2=3;\ a_3=5;\ ...;\ a_(100)=199\\\\S_n=(a_1+a_n)/(2)* n\\\\S_(100)=(1+199)/(2)*100=200*50=\boxed{10,000}`