# 일반수학및실습2-10.2절

## 2142 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 "", line 1, in File "_sage_input_5.py", line 10, in 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 File "/tmp/tmpVFOgdT/___code___.py", line 4, in exec compile(u'sum(_sage_const_1 /k, k, _sage_const_1 , oo) File "", line 1, in 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