Mathematics is the study of quality, structure, space and development. Mathematicalians, with rigorous deduction from appropriately selected axioms and definitions, search for patterns, make new conjectures, and create the truth.

In this research paper deals with maths for the rural people to do the maths as easiest way and integrated with some applications. And few problems are solved with easier ways.

This demonstrates proof through the use of successive divisions of a triangle, showing that the total of the alternating geometric sequence, all with the same base, equals the sum ^[1].