# Tagged Questions

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### How does a sequence's convergency change finite sums?

What has been troubling me lately is that I cannot grasp how a finite series could ever diverge if a finite sequence that is divergent can only imply to a finite sum every time. Perhaps my main ...
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### Insert Means in an Arithmetic Sequence (that contains logarithms)

So the question is: You have an Arithmetic Sequence. Log 2 and Log 1024 are two terms in the sequence Find 8 arithmetic means between them.
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### Finding the fifth term of this arithmetic progression problem

If the sum of the first 10 term is equal to $-240$ and the 7th term is $48$. How to find the 5th term?
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### Derive a formula to get the particular value from table

I have a table of points earned given the final game score. ...
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### proof by maths induction

not sure how to prove this: for all positive intergers prove: $$1+2(2)+3(2^2)+...+n(2^{n-1})=(n-1)(2^n)+1$$ heres my try: prove $n=1$ : 1=1 ...
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### Complex numbers summation

Sum the series $$\sum_{r=0}^n {{n}\choose{r}} \sin(\alpha +r\beta)$$ I've been using the C+jS method where C is the cosine series and S is the sine series and forming a result from there but have not ...
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### a problem on arithmetic progression,it is a very confusing sum

In an arithmetic progression,the sum of five terms is equal to 1\4 of the next five terms,prove that the 20th term is -112?
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### Sequence is periodic $x_{n+2}=|x_{n+1}-x_{n-1}|$

How to show that the sequence $$x_n, n \geq 0, x_{n+2}=|x_{n+1}-x_{n-1}|, n \geq 1$$ with $x_0, x_1, x_2$ positive integers, not all null, is periodic? I tried to pick up the square but obtained ...
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### Sum of G.P. terms to infinity when r $\lt$ 1

The sum of n g.p. terms with first term a and common ratio r is given by $$S_{n} = a\cdot\frac{1 - r^n}{1 -r} provided \ r \not= 1$$ But I'm confused as to what happen when r $\lt 1$. My module ...
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### Polynomials through successive differences

Let $h_0:\Bbb{N}\rightarrow\Bbb{N}$ be any function. Define recursively, for $m>0$, $$h_{r+1}(m)=h_r(m)-h_r(m-1).$$ Suppose that for some $k>0$ we have $h_k(m)\equiv d$ constant. Is this ...
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### Arithmetic progression question

In an arithmetic progression there are $2n$ arguments. The sum of last $n$ arguments is three times greater than that of the first n arguments. It is also known that the last argument in the series is ...
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### Is this geometric sequence convergent or divergent?

2, -6, 18, -54,... Is this geometric sequence convergent or divergent? I know that convergent sequences have terms that are approaching a constant, but how do I find out if that is the case? Thanks! ...
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### Bounding the sum of “almost” factorials

I am analyzing the complexity of an algorithm and the result is the sum of n products. Product 1 is the factorial. Product 2 is the factorial divided by 2. Product 3 is the factorial divided by 3 etc. ...
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### arithmetic and geometric progression

$a,b,c$ ,are consecutive arguments of a given arithmetic progression. $a^2, b^2, c^2$, are consecutive arguments of a geometric progression. With this information given, find the $q$ for the ...
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### Sum of a Hyper-geometric series. (NBHM 2011)

How to find the sum of the following series $$\frac{1}{5} - \frac{1\cdot 4}{5\cdot 10} + \frac{1\cdot 4\cdot 7}{5\cdot 10\cdot 15} - \dots\,.?$$ I have no idea. I have written the general ...
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### Determine positive integers

If $n\geq3$ is a positive integer, determine $n+1$ positive integers With the property that the sum of all $n$ integers from the $n+1$ numbers build the set: ...
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### Condition for a common root in two given quadratic equations

If $a,\;b,\;c$ are in Geometric Progression, then the equations $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$ have a common root if $\;\displaystyle\frac da,\;\frac eb,\;\frac fc$ are in: Arithmetic Progression ...
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### Find $x$ in $\large \,\, A^{A^{{{A^.}^.}^.}}= \,\,(\sqrt [x\cdot x\cdot x\cdot …] x)^{ (((1\cdot x+1)x +1)x +1)x+1…}$

If $\large \,\, A^{A^{{{A^.}^.}^.}}= \,\,(\sqrt [x\cdot x\cdot x\cdot ...] x)^{ (((1\cdot x+1)x +1)x +1)x+1...}$, and $\large \,\,A = (\sqrt[3]{3\sqrt 3 })^{\frac{\sqrt 3}{3}}$, find $x$ I have ...
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### Finding the value of a logarithmic expression involving an infinite GP

Find the value of $(0.16)^{\displaystyle\log_{2.5}(\frac13+\frac1{3^2}+\frac1{3^3}+\cdots)}$. I could solve the series. It gave $$(0.16)^{\log_{2.5}0.5}$$ Unable to proceed from here.
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### (Geometric) Sum of $100-50-25-(25/2)+\ldots+ (25/16)$

Determine the sum for this geometric series: $100-50+25-(25/2)+\ldots+ (25/16)$ I found $7$ to be the number of terms in this series, and the sum of the series to be $67.1875.$, but, the ...
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### Common difference between terms of the arithmetic progression

In an finite arithmetic progression: $S_5=55$, sum of the last five terms is 215 and total sum is $S_n=351$ . What is common difference between terms of the arithmetic progression? Why?
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### Could someone explain the algebra in this sequences problem?

$$\frac{(n^2+n)-n^2}{\sqrt{n^2+n}+n} = \frac{n}{n\left(\sqrt{1+\frac{1}{n}}+1\right)}$$ The advantage here is that the n's cancel, but I don't see why the argument of the sqrt() function ends up ...
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### Help find sum to infinity of a series - odd numbers with a common ratio

I am trying to derive the formula for the variance of a geometric distribution and am stuck at the following problem: I need to find the sum to infinity for the following series: ...
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### Finding $x$. The summation of the floor of the equation.

I would appreciate if somebody could help me with the following problem Q:Finding $x$. The summation of the floor of the equation. $$\sum_{i=1}^{2013}\left\lfloor\frac{x}{i!}\right\rfloor=1001$$
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### Math behind Keynesian Expenditure Multiplier

Take a look at this page: http://wiki.ubc.ca/Keynesian_Multiplier Why can you find out the sum of the geometric series just by dividing the mps by 1?
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I'm having trouble understanding how this expression: $$\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2+\dots}}}} \cdot ... 2answers 49 views ### Rational sequence with a_{n+1}=2a_n^2-1 Suppose we start with a rational number a_0, and define a_{n+1}=2a_n^2-1 for n\geq 0. For what a_0 will it be the case that a_i=a_j for some i\neq j? We can start with something like ... 1answer 60 views ### Sequence Puzzle If a_{0}= 1 , a_{1}=1, a_{n}=a_{n-1}a_{n-2}+1for n>1 then A) a_{465} is odd and a_{466} is even B) a_{465} is odd and a_{466} is odd C) a_{465} is even and a_{466} is even ... 1answer 71 views ### Solving this recursive function f(x)=f(x-k)+f(x/k). How to solve or simplify the following recursive function? f(x) is defined only for whole numbers as follows:$$f(x)=\begin{cases} 1 & \mbox{if } x<k; \\ f(x-k)+f(x/k) ...
Winston invests a sum of money at 6% per annum. How many years does it take him to double his money? I let the initial sum of money be $£a$. Then at the end of the first year, he has $£1.06a$ since ...