等差数列an中如果存在正整数k和L(k不等于L),使得前k项和Sk=k/L,前l项和SL=L/k,求Sk+L与4的关系,

Question

等差数列an中如果存在正整数k和L(k不等于L),使得前k项和Sk=k/L,前l项和SL=L/k,求Sk+L与4的关系,

Answer 1

Sk=ka1+k(k-1)d/2=k/La1+(k-1)d/2=1/L (1)SL=La1+L(L-1)d/2=L/ka1+(L-1)d/2=1/k (2)(1)-(2)(k-L)d/2=1/L-1/k(k-L)d/2 -(k-L)/kL=0(k-L)[(d/2)-1/(kL)]=0已知k≠L,k-L≠0,要等式成立,则d/2=1/(kL)代入(1)a1=1/L-(k-1)...