s=1-1⼀2+1⼀3-1⼀4+1⼀5....+1⼀31-1⼀32,试证明s<5⼀6

2024-12-13 04:21:23
推荐回答(2个)
回答1:

因为s=1/2+1/3-1/4+1/5....+1/31-1/32。
s=5/6-1/4+1/5....+1/31-1/32。
s=5/6-(1/4-1/5)-(1/6-1/7)-……-(1/30-1/31)-1/32.
因为(1/4-1/5),(1/6-1/7),……,(1/30-1/31),1/31都大于0,所以
s<5/6

回答2:

s=1-(1/2-1/3)-(1/4-1/5)-...-(1/30-1/31)-1/32
=1-1/6-1/20-....-1/(30x31)-1/32<1-1/6=5/6