#%%
import sympy as sp
import IPython.display as dp

k = sp.symbols("k")

# a)
print("a)")
dp.display(sp.Sum(k, (k, 4, 10)))
dp.display(sp.Sum(k, (k, 4, 10)).doit())

# b)
print("b)")
dp.display(sp.Sum(2*k, (k, 4, 10)))
dp.display(sp.Sum(2*k, (k, 4, 10)).doit())

# c)
print("c)")
dp.display(sp.Sum(k**3, (k, -2, 2)))
dp.display(sp.Sum(k**3, (k, -2, 2)).doit())

# d)
print("d)")
dp.display(sp.Sum(1/k, (k, 2, 4)))
dp.display(sp.Sum(1/k, (k, 2, 4)).doit())

# e)
print("3)")
dp.display(sp.Sum(2**k, (k, 0, 4)))
dp.display(sp.Sum(2**k, (k, 0, 4)).doit())

# f)
print("f)")
dp.display(sp.Sum(((-1)**k)*k, (k, 4, 9)))
dp.display(sp.Sum(((-1)**k)*k, (k, 4, 9)).doit())
#%%