1/4+1/28+1/70+.+1/9700 要过程 拜托啦~!

1/4+1/28+1/70+.+1/9700 要过程 拜托啦~!
1/4+1/28+1/70+.+1/9700 要过程 拜托啦~!

1/4+1/28+1/70+.+1/9700 要过程 拜托啦~!
1/4+1/28+1/70+……+1/9700
=1/(1×4)+1/(4×7)+1/(7×10)+……+1/(97×100)
=(1/3)×(1-1/4+1/4-1/7+1/7-1/10+……+1/97-1/100)
=(1/3)×(1-1/100)
=(1/3)×99/100
=33/100

原式=1/(1×4)+1/(4×7)+1/(7×10)+...+1/(97×100)
由于1/[n×(n+3)]=⅓[1/n-1/(n+3)]
∴原式=⅓(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)
=⅓(1-1/100)
=33/100