# Questions tagged [summation]

Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence

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### $\sum_{k=1}^{\infty }\left\lfloor\frac{5}{5^k}\right\rfloor$ giving wrong answer?

Bug introduced in 7.0 or earlier and fixed in 11.0.1 When I try to evaluate the following: $$\sum_{k=1}^{\infty }\Bigg\lfloor\frac{5}{5^k}\Bigg\rfloor$$ using ...
4k views

### How to differentiate formally?

I have been wrapping my head around this for a while now and I have not found a solution so far. I want to work with an arbitrary number of variables in Mathematica and use some built in functions. To ...
488 views

### sudden increase in timing when summing over 250 entries

I see a sudden increase of Timing by a factor of thousands when I sum over 250 elements of a matrix rather than over 249. So for instance, this table contains sums ...
298 views

### Why is “k” in the output of Sum[Log[k]/k^k, {k,1,Infinity}]?

Fixed in 11.3 NSum[Log[k]/k^k, {k,1,Infinity}, WorkingPrecision->50] (* 0.219947267975228664843531307905860703797097130 *) But ...
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### Sum or Product with Exclusions

Is there a built-in feature for handling things like: $$\sum_{\substack{i=0\\i\ne j}}^n\frac{a-a_i}{a_i-a_j}$$ and $$\prod_{\substack{i=0\\i\ne j}}^n\frac{a-a_i}{a_i-a_j}$$ or should I work out some ...
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### Ways to compute inner products of tensors

One way to evaluate the following sums is combining Table and Sum: $u_{abcd} = \sum_{e=1}^3 v_{aeb}w_{ced}$ $q_{ab} = \sum_{d,e=1}^3 v_{d e a}w_{deb}$ It will look like ...
3k views

### Mathematica thinks (-1)^n is non-real

When I ask Mathematica to evaluate NSum[((-1)^n)/n, {n, 1, 100}] it returns -0.688172 + 2.11297*10^-16 i Why is this? (-1)^n is either 1 or -1. I don't know why ...
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### Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. The expression is defined as follows: ...
491 views

### How to implement symbolic Ramanujan's summation in Mathematica?

How to implement Ramanujan's summation in symbolic form in Mathematica? For instance, I want as input the function $f(x)=x$, as output $-1/12$, as input $f(x)=1/x$, as output $\gamma$ (Euler's ...
157 views

### Bug in GeneratingFunction?

Bug introduced in 7.0 and fixed in 9.0.0 According to the documentation GeneratingFunction[a[n],n,x]==Sum[a[n]x^n,{n,0,Infinity}] However, for $a_n=1/(n+2)$ I ...
507 views

### Evaluating summations involving Fibonacci numbers in terms of Fibonacci numbers

There are many summations involving Fibonacci numbers which Mathematica 10.4 is able to evaluate directly in terms of Fibonacci numbers. For example, Mathematica evaluates the summation given below as ...
2k views

### SumConvergence[((-1)^n)/(Sqrt[n] + (-1)^n), n] returns True in Version 10.2?

Bug persisting through 10.4.1 I claim that the series $\sum_{n=2}^{\infty}\frac{(-1)^n}{\sqrt{n}+(-1)^n}$ diverges. To see this, rewrite the $n^{th}$ term as follows: \begin{equation*} \frac{(-1)^n}{\...
582 views

### How to find the sum for each individual row in a binary matrix until the first zero is reached from left to right.

I have a 150 by 300 binary matrix. I would like to sum the 1's for each individual row (from left to right) until the first zero is encountered. For example, if a given row is 1 1 1 1 1 1 0 0 0 1 0 0 ...
299 views

### Expand series unevaluated

I'm newbie in Mathematica. I'd like to obtain nice and verbose output for any series calculation. For example, given a simple sequence n*(-1)^(n-1) and ...
733 views

### RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
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### Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
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### Alternating sum

A frog is at the bottom of a 30 metre well. Each day it climbs 5 metres up the side, but it then slips back 3 metres each night. How long does it take to reach the top of the well? Is there an easier ...
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### Wolfram says sum diverges, but Mathematica gives a numerical value for infinite sum [closed]

Take this sum for example: $$\sum_{n=2}^\infty\frac1{\log(n!)}$$ Wolfram says that this does not converge by the comparison test. However, when I use Mathematica's ...
3k views

### Sum all numbers from 1 to 1000 divided by either 2,3,5 or 7

How do I find the sum all numbers from 1 to 1000 divided by atleast one of 2,3,5 or 7? EDIT: I am sorry for complicating this, but I need it to work for 10^11. So anything that requires too much heap ...
485 views

### Is it possible to find generating functions of infinite sequences with Mathematica?

I'm trying to find the generating function of a sequence as $(0,1,0,1,0,1,\dots)$ but reading Mathematica's help on FindGeneratingFunction[] seems to tell me that ...
337 views

### Error computing sum of sum of digits

I've defined a function that computes the sum of the base-b digits of n: DigitSum[n_, b_] := Total[IntegerDigits[n, b]] Then I defined a function that computes ...
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### What is wrong with my use of Summation?

I want to compute $r$ according to the following code: ...
359 views

### Differing answers when comparing Wolfram Alpha and Mathematica v.10.2

Out of curiousity, please consider following expression: Sum[(-1)^(n + 1)/n, {n, 1, 100000}] When evaluated using Wolfram Alpha: Result: ...
396 views

### Error in infinite sum [duplicate]

The binary weight of the non negative integer k is defined by w[k_] := Total[IntegerDigits[k, 2]] The first values are (cf. http://oeis.org/ A000120) ...
314 views

### How to represent integers using Egyptian fractions?

Let $N(n)$ be a set of integers, which can be presented using first $n$ Egyptian fractions: $$N(n):=\{m\in\mathbb{Z}:\ \ m=\sum_{i=1}^n\frac{\epsilon_i}{i},\ \epsilon_i=0\ \text{or}\ 1\}$$ I want ...