用简便方法计算1-2²+3²-4²+5²-6²+······+99²-100²
问题描述：
用简便方法计算1-2²+3²-4²+5²-6²+······+99²-100²
答
(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=-50...