Giải:
\(C=50^2-49^2+48^2-47^2+...+2^2-1^2\)
\(\Leftrightarrow C=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)
\(\Leftrightarrow C=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+...+\left(2-1\right)\left(2+1\right)\)
\(\Leftrightarrow C=1\left(50+49\right)+1\left(48+47\right)+...+1\left(2+1\right)\)
\(\Leftrightarrow C=\left(50+49\right)+\left(48+47\right)+...+\left(2+1\right)\)
\(\Leftrightarrow C=50+49+48+47+...+2+1\)
\(\Leftrightarrow C=\dfrac{\left(50+1\right).50}{2}\)
\(\Leftrightarrow C=1275\).
Chúc bạn học tốt!
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