Question

1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+...+1/60+...59/60怎么做

Answer 1

a1=1/2,a2=(1+2)/3,a3=(1+2+3)/4,...,an=(1+...+n)/(n+1),an=n(1+n)/2(n+1)=n/2,

sn=1/2(1+2+...+n)=1/4(n+1)n

s60=1/4(60*61)=15*61=915

1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+...+1/60+...59/60=915