因式分解1-2²+3²-4²+5²-6²+…+99²-100²+101²

问题描述:

因式分解1-2²+3²-4²+5²-6²+…+99²-100²+101²

1-2²+3²-4²+5²-6²+…+99²-100²+101² =(1-2)(1+2)+(3-4)(3+4)+...+(99-100)(99+100)+101²=-(1+2)-(3+4)+...-(99+100)+101²=-(1+100)×100/2+101²=-50×101+1...