关于函数展开成幂级数的这两个问题怎么计算?

要过程!!在线等!!急
2024-11-15 22:30:31
推荐回答(2个)
回答(1):

这两题都是凑等比数列求和公式

f(x)=1/(x^2+3x+2) =1/(x+1)-1/(x+2)
= 1/5 *1/(1-(x-4)/5) - 1/6 * 1/(1-(x-4)/6)
=1/5 sum((x-4)/5)^n) -1/6 sum((x-4)/6)^n
=sum[(x-4)^n (1/5^(n+1) -1/6^(n+1))
f(x)= (x-1 )/3* 1/(1-(x-1)/3)
=(x-1)/3 * sum(((x-1)/3)^n)
=sum(((x-1)/3)^(n+1))

回答(2):