Question

在1和100之间插入N个实数,使得N+2个数构成递增的等比数列 Tn为这N+2个数的乘积

Answer 1

令这个等比数列为bn,公比是q.则b1=1,b(n+2)=b1*q^(n+1)=100,q^(n+1)=100Tn=b1*b2*b3*...*b(n+2)=b1^(n+2)*q^(1+2+3+...+(n+1))=q^[(n+1)(n+2)/2]An=lgTn=lgq^[(n+1)(n+2)/2]=(n+2)/2*lgq^(n+1)=(n+2)/2*lg100=(n+2)/...