sicp-all-tasks/sicp/3_002e61

Exercise 3.61: Let 
  S
 be a power series
(Exercise 3.59) whose constant term is 1.  Suppose we want to find the
power series 
  
    1
    
      /
    
    S
  
, that is, the series 
  X
 such that 
  
    S
    X
    =
    1
  
.
Write 
  
    S
    =
    1
    +
    
      S
      R
    
  
 where 
  
    S
    R
  
 is the part of 
  S
 after the
constant term.  Then we can solve for 
  X
 as follows:

  
    
      
        S
        ⋅
        X
      
      
        =
      
      
        1
        ,
      
    
    
      
        (
        1
        +
        
          S
          R
        
        )
        ⋅
        X
      
      
        =
      
      
        1
        ,
      
    
    
      
        X
        +
        
          S
          R
        
        ⋅
        X
      
      
        =
      
      
        1
        ,
      
    
    
      
        X
      
      
        =
      
      
        1
        −
        
          S
          R
        
        ⋅
        X
        .
      
    
  

In other words, 
  X
 is the power series whose constant term is 1 and whose
higher-order terms are given by the negative of 
  
    S
    R
  
 times 
  X
.  Use
this idea to write a procedure invert-unit-series that computes 
  
    1
    
      /
    
    S
  

for a power series 
  S
 with constant term 1.  You will need to use
mul-series from Exercise 3.60.