Toán A = 100 + 98 + 96 + 94 … + 2 – 97 – 95 – 93 – … – 1 23/09/2021 By Vivian A = 100 + 98 + 96 + 94 … + 2 – 97 – 95 – 93 – … – 1
Đáp án: \(A=100.\) Giải thích các bước giải: \(\begin{array}{l} A = 100 + 98 + 96 + 94 + …. + 2 – 97 – 95 – 93 – …. – 1\\ = \left( {100 + 98 + 96 + 94 + …. + 2} \right) – \left( {97 + 95 + 93 + …… + 1} \right)\\ Dat:\,\,\,B = 100 + 98 + 96 + 94 + …. + 2\\ So\,\,cac\,\,so\,\,hang\,\,la:\,\,\,\,\frac{{100 – 2}}{2} + 1 = 50\,\,\,so\,\,hang.\\ \Rightarrow B = \frac{{\left( {100 + 2} \right).50}}{2} = 2550.\\ C = 97 + 95 + 93 + …… + 1\\ So\,\,\,cac\,\,\,so\,\,hang\,\,la:\,\,\,\frac{{97 – 1}}{2} + 1 = 49\,\,\,so\,\,hang.\\ \Rightarrow C = \frac{{\left( {97 + 1} \right).50}}{2} = 2450.\\ \Rightarrow A = B – C = 2550 – 2450 = 100. \end{array}\) Trả lời
Đáp án:
\(A=100.\)
Giải thích các bước giải:
\(\begin{array}{l} A = 100 + 98 + 96 + 94 + …. + 2 – 97 – 95 – 93 – …. – 1\\ = \left( {100 + 98 + 96 + 94 + …. + 2} \right) – \left( {97 + 95 + 93 + …… + 1} \right)\\ Dat:\,\,\,B = 100 + 98 + 96 + 94 + …. + 2\\ So\,\,cac\,\,so\,\,hang\,\,la:\,\,\,\,\frac{{100 – 2}}{2} + 1 = 50\,\,\,so\,\,hang.\\ \Rightarrow B = \frac{{\left( {100 + 2} \right).50}}{2} = 2550.\\ C = 97 + 95 + 93 + …… + 1\\ So\,\,\,cac\,\,\,so\,\,hang\,\,la:\,\,\,\frac{{97 – 1}}{2} + 1 = 49\,\,\,so\,\,hang.\\ \Rightarrow C = \frac{{\left( {97 + 1} \right).50}}{2} = 2450.\\ \Rightarrow A = B – C = 2550 – 2450 = 100. \end{array}\)