Question

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

Answer 1

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

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

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

\(=1.\left(1+2\right)+1.\left(3+4\right)+...+1.\left(99+100\right)\)

\(=1.\left(1+2+3+...+99+100\right)\)

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

\(=101.50\)

\(=5050\)

Tham khảo nhé~