并项求和法:求和:S=1-2+3-4+…+(-1)n+1n.
问题描述:
并项求和法:求和:S=1-2+3-4+…+(-1)n+1n.
答
令S=1-2+3-4+…+(-1)n+1n=(1-2)+(3-4)+…+(-1)n(n-1)+(-1)n+1n,当n为偶数时,令S=(1-2)+(3-4)+…+[(n-1)-n]=-1×n2,即sn=-n2当n为奇数时,S=(1-2)+(3-4)+…+[(n-2)-(n-1)]+n=-1×n-12+n...