设f(n)=1+1/2+1/3+1/4+…+1/2n,则f(k+1)-f(k)= _ .
问题描述:
设f(n)=1+
+1 2
+1 3
+…+1 4
,则f(k+1)-f(k)= ___ .1 2n
答
当n=k+1时,f(k+1)=1+12+13+14+…+12k+1,当n=k时,f(k)=1+12+13+14+…+12 k,则f(k+1)-f(k)=1+12+13+14+…12 k+12 k+1+…+12k+1-(1+12+13+14+…+12 k)=12k+1+12k+2+…+12k+1,故答案为:...