All Questions
20
questions
1
vote
1
answer
102
views
Why is this summation formula wrong?
This is the alternate form of the summation formula:
$$
\sum^{n}_{k=0} a(c)^k = \frac{ac^{n+1} - a}{c - 1}
$$
so why is this wrong?
$$
\sum^{n}_{k=0} (-\frac{1}{2})^k = \frac{(-\frac{1}{2})^{n+1} - ...
- 1,085
3
votes
5
answers
5k
views
Deriving the summation formula for $x^2, x^3,\ldots,x^n$
How is the summation formula's for $x,x^2,x^3,x^4,\ldots$ derived? I know how to do it for $x$ which is $n^2/2 + n/2$ but I am having hard time deriving the summation formula for $x^n$ on my own. I ...
- 835
1
vote
4
answers
957
views
Summation of n-squared, cubed, etc. [duplicate]
How do you in general derive a formula for summation of n-squared, n-cubed, etc...? Clear explanation with reference would be great.
- 493
17
votes
7
answers
8k
views
Chain rule for discrete/finite calculus
In the context of discrete calculus, or calculus of finite differences, is there a theorem like the chain rule that can express the finite forward difference of a composition $∆(f\circ g)$ in ...
- 1,787
11
votes
9
answers
6k
views
How to compute the formula $\sum \limits_{r=1}^d r \cdot 2^r$?
Given $$1\cdot 2^1 + 2\cdot 2^2 + 3\cdot 2^3 + 4\cdot 2^4 + \cdots + d \cdot 2^d = \sum_{r=1}^d r \cdot 2^r,$$
how can we infer to the following solution? $$2 (d-1) \cdot 2^d + 2. $$
Thank you
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