CODEWITHSUNDEEP
python
Varun
Varun

Reputation: 1043

Sum of given series

I am trying to find the sum for series : 1 − 1 / 2 + 1 / 3 − 1 / 4 + · · · + 1 / 99 − 1 / 100 ** 2 with python.

My code is - 

psum = 0
nsum = 0
for k in range(1,100):
    if k%2 == 0:
        nsum += 1.0/k
    else:
        psum += 1.0/k

print psum - nsum - 1.0/100**2

The output is 0.69807217931

I don't have the answer and just want to verify if I am doing it right.

This is not a homework question but just random Python practice.

Upvotes: 4

Views: 8414

Answers (5)

asafm
asafm

Reputation: 921

Here's my suggestion. little but more LOC then @steveha but more generic.

getx=lambda x:(1.0/x)*((-1)**((x%2)+1))
num=100
sum((getx(x) for x in xrange(1,num)))+getx(num)**2
0.688172179310195

Upvotes: 0

steveha
steveha

Reputation: 76695

sum(1.0/k if k % 2 else -1.0/k for k in xrange(1, 100)) - 1.0/100**2

The above code does the same thing as your code, and gets the same answer.

Why does the series use 1/k from 1 through 99, and then use 1/k**2 just for k == 100?

Upvotes: 3

georg
georg

Reputation: 214949

Well, I believe

import math
print math.log(2)

would do the trick.

Upvotes: 4

Aaron Sokoloski
Aaron Sokoloski

Reputation: 71

The easiest way to see if you're doing it right is to try it with a much shorter series, one that you can check by hand. For example, use range(1, 5) and see if it gives the answer you expect.

For style tips, you can use xrange instead of range. xrange is nice because it just returns each number as it's needed, while range creates a big list of all the numbers. If you did this for range(1, 1000000), it would use up a lot of memory, while xrange wouldn't.

You could also get away with just one variable for the sum instead of two, I think.

Upvotes: 1

Karl Knechtel
Karl Knechtel

Reputation: 61478

That works fine, but why not just use one "summing" variable (call it total, as a matter of good practice, since there is a built-in called sum which you don't really want to hide), and actually add or subtract from it at each step?

Alternately (pun intended!), actually use that sum function. The range function can be used to skip every other number, too.

>>> sum(1.0/k for k in range(1, 100, 2)) - sum(1.0/k for k in range(2, 100, 2)) - (1.0/100**2)
0.6980721793101952

Or, as steveha shows, you can use logic to sort out whether to add or subtract the number based on whether it's divisible by 2, and handle it with a "weighted" sum (adding 1.0/k or -1.0/k as appropriate). This is why you should learn more math as a programmer :)

Upvotes: 5

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