请问如何证明无穷级数1/2+1/4+1/8+1/16+1/32+…………的和为1?
问题描述:
请问如何证明无穷级数1/2+1/4+1/8+1/16+1/32+…………的和为1?
答
1/2+1/4+1/8+1/16+1/32+…+1/2^n
=1-1/2^n
当n无限大时,1/2^n=0
所以无穷级数1/2+1/4+1/8+1/16+1/32+…的和为1