︠04f41261-8a9f-44a8-9ec5-c5954d1180d3s︠
%typeset_mode True
︡621e77be-63c1-44b8-9fd8-f488806689bf︡{"done":true}︡
︠34346a49-6663-458f-a023-f05c8087789as︠
g(x) = (1/2)*(x^-3)
︡33e886d2-aa85-4bc7-9fc5-5f0419accc67︡{"done":true}︡
︠37dccb66-b7a2-4f02-8668-5886d62c74e0s︠
g(x)
︡aea5a0e9-3714-4d84-b9f5-96f51dc02d68︡{"html":"
$\\displaystyle \\frac{1}{2 \\, x^{3}}$
"}︡{"done":true}︡
︠e3361f9f-ecac-44af-8d0f-4b5667353759s︠
integral(g(x),x)
︡274db6af-0d42-47b7-b595-aec97a567843︡{"html":"$\\displaystyle -\\frac{1}{4 \\, x^{2}}$
"}︡{"done":true}︡
︠e403012b-19df-4cf0-98ac-9a04411943f8s︠
integral(g(x),x,4,7)
︡26fa3695-9038-4478-a066-499b1177ceb3︡{"html":"$\\displaystyle \\frac{33}{3136}$
"}︡{"done":true}︡
︠3cdfa673-d6e8-44b2-8358-cddaec18ab9ds︠
f(x) = e^(2*x)
︡db7648f3-1352-4b46-894f-7654dcd2722c︡{"done":true}︡
︠3e72c490-9bac-4abd-98df-a3a5514464e6s︠
integral(f(x),x)
︡71ee139f-7e28-4222-b723-8a080acf506c︡{"html":"$\\displaystyle \\frac{1}{2} \\, e^{\\left(2 \\, x\\right)}$
"}︡{"done":true}︡
︠e25c5816-b542-400a-92cf-550d8ab66dbcs︠
var('p')
︡0ee22c53-0a28-4869-8221-63fc1b08a8b7︡{"html":"$\\displaystyle p$
"}︡{"done":true}︡
︠5f21fa8a-321e-4cd0-8ceb-4b408975c5ccs︠
integral(p/x^2,x,1,infinity)
︡773a3eb8-3b87-4b0c-a8f1-e03140df30a9︡{"html":"$\\displaystyle p$
"}︡{"done":true}︡
︠38c3b0bf-9c2d-401c-b1ac-25c1a42dcb18s︠
a(n) = 7*(1/3)^(n-1)
def s(k):
return sum([a(n) for n in [1..k]])
︡0804c432-e0f2-4ed7-a4d3-0e6badb2bf67︡{"done":true}︡
︠41c88aca-18e1-4f7c-8ad8-8b6809cd51a3s︠
s(1)
︡ff60f44a-b020-44f9-8370-c5ec86608535︡{"html":"$\\displaystyle 7$
"}︡{"done":true}︡
︠73add27c-cdce-4668-b3a9-8c3703724365s︠
s(2)
︡1985e80b-20ee-47ea-9958-464934593748︡{"html":"$\\displaystyle \\frac{28}{3}$
"}︡{"done":true}︡
︠21165f9e-0ed1-4bb5-b4bb-969e7ea9a681s︠
s(3)
︡8f1ac6c0-ef1d-409c-9177-2d5a0eaf73d2︡{"html":"$\\displaystyle \\frac{91}{9}$
"}︡{"done":true}︡
︠b985bd6a-7940-4cc0-aab7-284bd269ec42s︠
N(s(300), digits=300)
︡db052945-b149-47e6-8924-0a41d23d9642︡{"html":"$\\displaystyle 10.4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999232969058979478899263634287904603903715132946830131371516323094187830771103701176980793206438309762743975141858970313405006263004769472620836663078953524558$
"}︡{"done":true}︡
︠3a4fc9f0-e6e1-4a3e-b211-0784b3b67d3fs︠
︡841c6474-050f-4413-9b85-5c03bfa99f31︡{"done":true}︡
︠8cbb3d5c-4346-4874-bb6a-cf64167b056fs︠
︡a6ed44e9-257c-4c32-9280-ee8ac45c97b6︡{"done":true}︡
︠7dd6cdf9-f906-446d-a0d0-4374a41fca69︠