given an = 1/2n

Question

a) show that an —> 0

b) plot the first 50 terms of the sequence (starting n=1) and the first 50 partial sums on the same graph

c) does the series converges or diverge? verify by taking the sum using sp.summation().

Answer 1

# a) given a = (1/2n) show that a —> 0

# let's loop through the first 10 terms

for i in range(1,11):

print(1/(2*i))

# b) plot the first 50 terms of the sequence (starting n=1) and the first 50 partial sums on the same graph

import matplotlib.pyplot as plt

fig, ax = plt.subplots()

x = range(1,51)

a_vals= [1/(2*i) for i in range(1,51)]

ax.plot(x, a_vals);

# c) does the series converges or diverge? verify by taking the sum using sp.summation().

import sympy as sp

# define symbols

n = sp.symbols('n')

# Calculate the sum to determine convergence or divergence

sp.summation(1/(2*n), (n, 1, sp.oo))