作业帮给定正整数n和实数M,对于满足条件:(a1)^2+[a(n+1)]^2≤M^2的所有等差数列:a1,a2,a3….,试求S=a(n+1)+a(n+2)+……+a(2n+1) 的最大值.
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/12 09:16:43
![给定正整数n和实数M,对于满足条件:(a1)^2+[a(n+1)]^2≤M^2的所有等差数列:a1,a2,a3….,试求S=a(n+1)+a(n+2)+……+a(2n+1) 的最大值.](/uploads/image/z/7099830-54-0.jpg?t=%E7%BB%99%E5%AE%9A%E6%AD%A3%E6%95%B4%E6%95%B0n%E5%92%8C%E5%AE%9E%E6%95%B0M%2C%E5%AF%B9%E4%BA%8E%E6%BB%A1%E8%B6%B3%E6%9D%A1%E4%BB%B6%3A%28a1%29%5E2%2B%5Ba%28n%2B1%29%5D%5E2%E2%89%A4M%5E2%E7%9A%84%E6%89%80%E6%9C%89%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%3Aa1%2Ca2%2Ca3%E2%80%A6.%2C%E8%AF%95%E6%B1%82S%3Da%28n%2B1%29%2Ba%28n%2B2%29%2B%E2%80%A6%E2%80%A6%2Ba%282n%2B1%29+%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC.)
给定正整数n和实数M,对于满足条件:(a1)^2+[a(n+1)]^2≤M^2的所有等差数列:a1,a2,a3….,试求S=a(n+1)+a(n+2)+……+a(2n+1) 的最大值.
给定正整数n和实数M,对于满足条件:(a1)^2+[a(n+1)]^2≤M^2的所有等差数列:a1,a2,a3….,试求S=a(n+1)+a(n+2)+……+a(2n+1) 的最大值.
给定正整数n和实数M,对于满足条件:(a1)^2+[a(n+1)]^2≤M^2的所有等差数列:a1,a2,a3….,试求S=a(n+1)+a(n+2)+……+a(2n+1) 的最大值.
解法一 由Cauchy不等式求解
S=a(n+1)+a(n+2)+……+a(2n+1)
=(n+1)*[a(n+1)+a(2n+1)]/2
=(n+1)*[3a(n+1)-a1]/2
=