Question

a1=3分之一，a2=15分之1，a3=35分之1，求a1+a2+a3+...+a100的值

过程

Answer 1

解：由题意，得
a1=1/(1*3)=1/2*(1-1/3)
a2=1/(3*5)=1/2*(1/3-1/5)
^
a100=1/2*(1/(2n-1)-1/2n+1))
所以a1+a2+a3+...+a100=1/2*(1-1/3+1/3-1/5+^+1/(2n-1)-1/(2n+1)))
=1/2*(1-1/(2n+1))
=2n/(2n+1)

Answer 2

解：原式=1/(1×3）﹢1/（3×5）+1/(5×7）+……+1/(199×201)
=1/2[1-1/3+1/3-1/5+1/5-1/7+……+1/199-1/201)
=1/2(1-1/201)
=100/201