Question

与X轴，Y轴围成的三角形面积为S 【当K=1时，三角形面积为S1;当K =2时，三角形面积为S2

Answer 1

另x=0,y= 1÷（k+1);y=0,x= -1÷k

故S=1/2÷（k+1) ÷k

=1/2*（1/k-1/(k-1))

显然分母为等差数列,只要错位求和,很容易得到：

s1+s2+``````sn=1/2(1/(1*2)+1/(2*3)+``````1/(n(n+1)))

=1/2(1-1/2+1/2-1/3+``````1/n-1/(n+1))

=1/2(1-1/(n+1))

=n/2(n+1)