用简便方法计算1-2²+3²-4²+5²-6²+······+99²-100²

用简便方法计算1-2²+3²-4²+5²-6²+······+99²-100²
用简便方法计算1-2²+3²-4²+5²-6²+······+99²-100²

用简便方法计算1-2²+3²-4²+5²-6²+······+99²-100²
(1-2²)+(3²-4²)+(5²-6²)+······+(99²-100²)
=∑((2n-1)²-(2n)²),n=1,2,3,4,.,50
=∑(1-4n),n=1,2,3,4,.,50
=((1-4*1)+(1-4*50))*50/2
=(-3-199)*50/2
=-202*50/2
=-5050