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%typeset_mode True

g(x) = (1/2)*(x^-3)

g(x)
12 x3\displaystyle \frac{1}{2 \, x^{3}}
integral(g(x),x)
−14 x2\displaystyle -\frac{1}{4 \, x^{2}}
integral(g(x),x,4,7)
333136\displaystyle \frac{33}{3136}
f(x) = e^(2*x)

integral(f(x),x)
12 e(2 x)\displaystyle \frac{1}{2} \, e^{\left(2 \, x\right)}
var('p')
p\displaystyle p
integral(p/x^2,x,1,infinity)
p\displaystyle p
a(n) = 7*(1/3)^(n-1)
def s(k):
    return sum([a(n) for n in [1..k]])

s(1)
7\displaystyle 7
s(2)
283\displaystyle \frac{28}{3}
s(3)
919\displaystyle \frac{91}{9}
N(s(300), digits=300)
10.4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999232969058979478899263634287904603903715132946830131371516323094187830771103701176980793206438309762743975141858970313405006263004769472620836663078953524558\displaystyle 10.4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999232969058979478899263634287904603903715132946830131371516323094187830771103701176980793206438309762743975141858970313405006263004769472620836663078953524558