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Sum of 1's: Algebra Problem Find the sum: 1+111+11111+1111111+…..1….111(2k+1) ones  Useful points: Try with Hints ... Other Useful Links GCD and Bezout Theorem Gauss Trick of Algebra Related Program Subscribe to Cheenta at YouTube

Understand the problem Let O be a point inside a parallelogram ABCD such that \(\angle AOB+\angle COD =180\) prove that \(\angle OBC =\angle ODC\) Useful Points Suggested book Challenges and Thrills in Pre-College Mathematics Try with Hints... Other Useful Links GCD and Bezout Theorem Gauss Trick of Algebra Related Program Subscribe to Cheenta at YouTube

This problem from ISI Entrance 2019 is an interesting application of complex numbers in geometry. Try your hands on this!

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1996 based on Amplitude and Complex numbers.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1996 based on Roots of Equation and Vieta's formula.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Tetrahedron Problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Triangle and integers.

Try this problem from Singapore Mathematics Olympiad, SMO, 2018 based on Functional Equation. You may use sequential hints if required.

Try this beautiful problem from Algebra: Arithmetic sequence from AMC 10A, 2015, Problem. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and the greatest integer.

Try this beautiful problem from Mensuration: Problem based on Cylinder from AMC 10A, 2015. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Series and sum.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Rectangles and sides.