Question

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100² -99² +98² -97^{2 .........+ ₂2-₁2}

Answer 1

\(100^2-99^2+98^2-97^2+....+2^2-1^2\)

\(=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=100+99+98+97+...+2+1\)

\(=\frac{\left(100+1\right)\cdot100}{2}=5050\)