일반수학및실습2-10.2절

2094 days 전, jhlee2chn 작성

var('n') a(n)=3*n^2/(7*n^2+1) limit(a(n), n=+oo) 
        
3/7
3/7

예제 5.
var('k') sum(1/k, k, 1, oo) 
        
#0: simplify_sum(expr='sum(1/k,k,1,inf))
Traceback (click to the left of this block for traceback)
...
ValueError: Sum is divergent.
#0: simplify_sum(expr='sum(1/k,k,1,inf))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_5.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyKCdrJykKc3VtKDEvaywgaywgMSwgb28p"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpVFOgdT/___code___.py", line 4, in <module>
    exec compile(u'sum(_sage_const_1 /k, k, _sage_const_1 , oo)
  File "", line 1, in <module>
    
  File "/usr/local/sage-5.12/local/lib/python2.7/site-packages/sage/misc/functional.py", line 654, in symbolic_sum
    return expression.sum(*args, **kwds)
  File "expression.pyx", line 9700, in sage.symbolic.expression.Expression.sum (sage/symbolic/expression.cpp:40331)
  File "/usr/local/sage-5.12/local/lib/python2.7/site-packages/sage/calculus/calculus.py", line 584, in symbolic_sum
    return maxima.sr_sum(expression,v,a,b)
  File "/usr/local/sage-5.12/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.py", line 788, in sr_sum
    raise ValueError, "Sum is divergent."
ValueError: Sum is divergent.

예제 8.
var('k') 3*sum((1/8)^k, k, 1, oo)-5*sum((1/3)^k, k, 1, oo) 
        
-29/14
-29/14

예.
var('k, n') par=sum(1/((k+2)*(k+3)), k, 1, n) print "Partial Sum=", par 
        
Partial Sum= 1/3*n/(n + 3)
Partial Sum= 1/3*n/(n + 3)
limit(par, n=oo) 
        
1/3
1/3
sum(1/((k+2)*(k+3)), k, 1, oo) # 직접 구할 수도 있음 
        
1/3
1/3