Question

Tính : A = 1.99 + 2.98 + 3.97 + ........+ 97.3 + 98.2 + 99.1

Answer 1

\(A = 1.99 + 2.98 + 3.97 + ...+ 97.3 + 98.2 + 99.1\)

\(A=1.99+2.\left(99-1\right)+3.\left(99-2\right)+...+98.\left(99-97\right)+99.\left(99-98\right)\)

\(A=1.99+2.99-1.2+3.99-2.3+98.99-97.98+99.99-98.99\)

\(=\left(1.99+2.99+3.99+...+98.99+99.99\right)-\left(1.2+2.3+3.4+...+97.98+98.99\right)\)

\(=99.\left(1+2+3+...+98+99\right)-\left(1.2+2.3+3.4+...+97.98+98.99\right)\)

\(=99.4950-\left(1.2+2.3+3.4+97.98+98.99\right)\)

Mà \(1.2+2.3+3.4+...97.98+98.99\)

\(=\frac{1}{3}.\left[1.2+2.3.\left(4-1\right)+3.4.\left(5-2\right)+98.99.\left(100-97\right)\right]\)

\(=\frac{1}{3}.98.99.100=323400\)

\(\Rightarrow A=99.4950-323400=166650\)