Question

无穷等比数列的公比为q，任意一项都等于其后所有项和的k倍，则k的取值范围

Answer 1

a1=k*a2/(1-q),-1<q<1且q≠1,k=(1-q)/q,k>o或k<－2

Answer 2

an=ka(n+1)*lim(1-q^i)/(1-q), i趋向无穷大
1=kq*lim(1-q^i)/(1-q), i趋向无穷大
k=1/[q*lim(1-q^i)/(1-q)], i趋向无穷大
k的最大值为1/q
当q<1时,k的取值范围为((1-q)/q,1/q)
当q>1时,k的取值范围为(0,1/q)