０４/０３/１７８ ＭＡＴＨ ＪＪ

diatomss

178. 数列1, 2,3,5,8,13,…(an=an-1+an-2)求s52=a1+a2+…+a52 橙子评价:感谢coolerdavid提供思路,a3=a2+a1,a4=a3+a2,a5=a4+a3....a54=a53+a52,change ta3-a2=a1,a4-a3=a2,a5-a4=a3....a54-a53=a52.the add both sides together.you will find s=a54-2.

斑竹请教Ａ５４怎么求出，我想了半天也没看出规律来，帮帮我好吗？

谢谢

diatomss

thanks    a     lot    !!!!

himba

if arrange the equations this way,

a3 - a2 = a1 a4 - a3 = a2 a5 - a4 = a3 ... a53 - a52 = a51 a54 - a53 = a52

add up everything on the left hand side and everything on the right hand side respectively, you will get

a54 - a2 = a1 + a2 + a3 + ... + a51 + a52 = s52