Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 based on Theory of Equations.
The expressions A=\(1\times2+3\times4+5\times6+...+37\times38+39\)and B=\(1+2\times3+4\times5+...+36\times37+38\times39\) are obtained by writing multiplication and addition operators in an alternating pattern between successive integers.Find the positive difference between integers A and B.
Series
Equations
Number Theory
Answer: is 722.
AIME I, 2015, Question 1
Elementary Number Theory by Sierpinsky
A = \((1\times2)+(3\times4)\)
\(+(5\times6)+...+(35\times36)+(37\times38)+39\)
B=\(1+(2\times3)+(4\times5)\)
\(+(6\times7)+...+(36\times37)+(38\times39)\)
B-A=\(-38+(2\times2)+(2\times4)\)
\(+(2\times6)+...+(2\times36)+(2\times38)\)
=722.