A = 100 + 98 + 96 + 94 ... + 2 - 97 - 95 - 93 - ... - 1

Đáp án:

\(A=100.\)

Giải thích các bước giải:

\(\begin{array}{l} A = 100 + 98 + 96 + 94 + .... + 2 - 97 - 95 - 93 - .... - 1\\ = \left( {100 + 98 + 96 + 94 + .... + 2} \right) - \left( {97 + 95 + 93 + ...... + 1} \right)\\ Dat:\,\,\,B = 100 + 98 + 96 + 94 + .... + 2\\ So\,\,cac\,\,so\,\,hang\,\,la:\,\,\,\,\frac{{100 - 2}}{2} + 1 = 50\,\,\,so\,\,hang.\\ \Rightarrow B = \frac{{\left( {100 + 2} \right).50}}{2} = 2550.\\ C = 97 + 95 + 93 + ...... + 1\\ So\,\,\,cac\,\,\,so\,\,hang\,\,la:\,\,\,\frac{{97 - 1}}{2} + 1 = 49\,\,\,so\,\,hang.\\ \Rightarrow C = \frac{{\left( {97 + 1} \right).50}}{2} = 2450.\\ \Rightarrow A = B - C = 2550 - 2450 = 100. \end{array}\)