用简便计算1+1/2+1/4+1/8+1/14+1/22+1/32+1/44+1/58+1/74要有计算过程

问题描述:

用简便计算1+1/2+1/4+1/8+1/14+1/22+1/32+1/44+1/58+1/74
要有计算过程

前四项等于1+1/2+1/2-1/4+1/4-1/8=2-1/8=15/8.后面慢慢加。

1+1/2+1/4+1/8+1/14+1/22+1/32+1/44+1/58+1/74
=2-1/8+1/32+1/(2*7)+1/(2*11)+1/(4*11)+1/(2*29)+1/(2*37)
=2+(-330484+82621+188848+120176+60088+45584+35728)/(32*7*11*29*37)
=2+202561/2643872.