Direct summation: - 1 & # 178; + 2 & # 178; - 3 & # 178; + 4 & # 178; - 5 & # 178; + 6 & # 178; - ······· - 99 & # 178; + 100 & # 178; | Math enthusiast | Mathematical art

Direct summation: - 1 & # 178; + 2 & # 178; - 3 & # 178; + 4 & # 178; - 5 & # 178; + 6 & # 178; - ······· - 99 & # 178; + 100 & # 178;

=(- 1 & # 178; + 2 & # 178;) + (- 3 & # 178; + 4 & # 178;) + (- 5 & # 178; + 6 & # 178;) - ······ (- 99 & # 178; + 100 & # 178;) = (2 + 1) (2-1) + (4 + 3) + (4-3) +, + (100 + 99) + (100-99) = 1 + 2 + 3 + 4 +... + 99 + 100 = (1 + 100) + (2 + 99) +... + (50 + 51) = 101x50 = 5050, hope to help

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