作业帮A=48乘以1/[3的平方-4]+1/[4的平方-4]+...+1/[100的平方-4]】与A最接近的正整数是
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/13 14:35:25
![A=48乘以1/[3的平方-4]+1/[4的平方-4]+...+1/[100的平方-4]】与A最接近的正整数是](/uploads/image/z/142388-44-8.jpg?t=A%3D48%E4%B9%98%E4%BB%A51%2F%5B3%E7%9A%84%E5%B9%B3%E6%96%B9-4%5D%2B1%2F%5B4%E7%9A%84%E5%B9%B3%E6%96%B9-4%5D%2B...%2B1%2F%5B100%E7%9A%84%E5%B9%B3%E6%96%B9-4%5D%E3%80%91%E4%B8%8EA%E6%9C%80%E6%8E%A5%E8%BF%91%E7%9A%84%E6%AD%A3%E6%95%B4%E6%95%B0%E6%98%AF)
A=48乘以1/[3的平方-4]+1/[4的平方-4]+...+1/[100的平方-4]】与A最接近的正整数是
A=48乘以1/[3的平方-4]+1/[4的平方-4]+...+1/[100的平方-4]】与A最接近的正整数是
A=48乘以1/[3的平方-4]+1/[4的平方-4]+...+1/[100的平方-4]】与A最接近的正整数是
1/[(n+2)^2-4] = 1/[n(n+4)] = (1/4)[1/n - 1/(n+4)],
A = 48[1/[3^2-4] + 1/[4^2-4]+1/[5^2-4]+1/[6^2-4]+1/[7^2-4]+...+1/[95^2-4]+1/[96^2-4]+1/[97^2-4]+1/[98^2-4]+1/[99^2-4]+1/[100^2-4]
=48/4[1/1 - 1/5 + 1/2 - 1/6 + 1/3 - 1/7 + 1/4 - 1/8 + 1/5 - 1/9 + ...+ 1/93-1/97 + 1/94-1/98 + 1/95-1/99 + 1/96-1/100 + 1/97-1/101 + 1/98-1/102]
=12[1/1 + 1/2 + 1/3 + 1/4 - 1/99 - 1/100 - 1/101 - 1/102]
= 12 + 6 + 4 + 3 - 12/99 - 12/100 - 12/101 - 12/102
= 25 - 12[1/99 + 1/100 + 1/101 + 1/102],
A > 25 - 12[4/99] = 25 - 48/99,
A < 25 - 12[4/102] = 25 - 48/102.
-48/99 < A - 25 < -48/102,
51/99 < A - 24 < 54/102,
48/102 < 25-A < 48/99 < 51/99 < A - 24 < 54/102.
A与25 更接近.
与A最接近的正整数为25.