All Questions
20
questions
0
votes
4
answers
114
views
Find the sum of the first $50$ terms of the series $a_{n} = -4a_{n-1} + 3$.
I'm not sure where to start this without being given some terms.
Find the sum of the first $50$ terms of the series $$a_{n} = -4a_{n-1} + 3$$ I can see that the common difference is $-4$ and the slope ...
- 172
0
votes
1
answer
62
views
How to get $A$ and $B$ from $A\csc 10^\circ+B=$ $\sin 10^\circ+\cos 60^\circ+\cos 40^\circ+\sin 70^\circ+\sin 90^\circ$?
The problem is as follows:
Find $A+B$ from:
$A\csc 10^\circ+B=\sin 10^\circ+\cos 60^\circ+\cos 40^\circ+\sin 70^\circ+\sin 90^\circ$
The alternatives given in my book are as follows:
$\begin{array}{ll}...
- 4,185
1
vote
3
answers
55
views
Step in proof of derivation of $1+2+\cdots+n=\tfrac{n(n+1)}{2}$.
I have been solving a few computer science problems lately and it is important for me to understand how the time complexity of an algorithm is calculated by coming up with the derivation and arriving ...
- 113
1
vote
3
answers
978
views
Sum of all the numbers in the grid.
A square containing numbers
$$
\begin{array}{|c|c|c|}
\hline 1 & 2 & 3 \\ \hline
1 & 2 & 2 \\ \hline
1 & 1 & 1 \\\hline
\end{array}
\qquad \qquad\qquad
\begin{array}{|c|c|c|c|...
0
votes
2
answers
332
views
Find the $n^{th}$ term and the sum to $n$ terms of the following series
Find the $n^{th}$ term and sum to $n$ terms of the following series.
$$1.3+2.4+3.5+……$$
My Attempt:
Here,
$n^{th}$ term of $1+2+3+……=n$
$n^{th}$ term of $3+4+5+……=n+2$
Thus,
$n^{th}$ term of the ...
- 7,426
0
votes
5
answers
334
views
Find the sum to $n$ terms of the following series
Find the sum to $n$ terms of the following series:
$$\dfrac {2}{5}+\dfrac {6}{5^2}+\dfrac {10}{5^3}+\dfrac {14}{5^4}+………$$
My Attempt:
Let
$$S_n=\dfrac {2}{5} + \dfrac {6}{5^2}+\dfrac {10}{5^3}+\...
- 7,426
4
votes
3
answers
119
views
Find value of $a_{2012}$
A sequence $\left\{a_n\right\}$ is defined as:
$a_1=1$, $a_2=2$ and
$$a_{n+1}=\frac{2}{a_n}+a_{n-1}$$ $\forall$ $n \ge 2$
Find $a_{2012}$
My Try:
we have
$$a_{n+1}-a_{n-1}=\frac{2}{a_n}$$
$$...
- 13.2k
0
votes
4
answers
762
views
How does one evaluate $1+2-3-4+5+6-7-8+\cdots+50$?
How does one evaluate the sum $1+2-3-4+5+6-7-8+\cdots+50$?
I know how to find the sum of arithmetic progressions: without the negative signs, one simply has
$$
1+2+\cdots+50=\frac{1}{2}\cdot(1+50)\...
- 109
2
votes
2
answers
103
views
Find the value of $\sum_{p=0}^{\infty}\sum_{q=0}^{\infty} \frac{2^{-p-q}}{1+p+q}$
Find the value of
$$S=\sum_{p=0}^{\infty}\sum_{q=0}^{\infty} \frac{2^{-p-q}}{1+p+q}$$
In the second summation i used change of variable $p+q+1=r$ then we get
$$S=\sum_{p=0}^{\infty}\:\sum_{r=p+1}^...
- 13.2k
0
votes
4
answers
185
views
Solving $\left(1+3+5...+(2n+1)\right ) + \left(3.5+5+6.5+...+(\frac{7+3n}{2})\right)=105$ [closed]
$\left(1+3+5...+(2n+1)\right ) + \left(3.5+5+6.5+...+(\frac{7+3n}{2})\right)=105$
It is the equation that I did not understand how to find $n.$
user491034
2
votes
1
answer
2k
views
Arithmetic Series: find the sum of 25 terms given 2 terms and their values
I need help with this question:
"Find S25, given an arithmetic series whose 8th term is 16 and whose 13th term is 81."
What I did was:
1. Found the common difference (d) like this:
81 - 16 = 65
...
0
votes
5
answers
1k
views
Pre-calculus- Finding the sum of $1.2+2.3x+3.4x^2...$ where $|x|<1$
Find the sum of $1.2+2.3x+3.4x^2...\infty$ where $|x|<1$
I have got the $\mathbb{n^{th}\quad term \quad= n(n+1)(x^{n-1})}$
Then I tried finding $\sum\limits_{k=1}^\infty n(n+1)(x^{n-1})$ but it's ...
- 6,111
1
vote
2
answers
54
views
Proof of a series involving Arithmetic Progression
If $${a}_{1},{a}_{2},{a}_{3},.....{a}_{n-1},{a}_{n} $$ are in A.P., then show that $$ \frac{1}{{a}_{1}{a}_{n}} + \frac{1}{{a}_{2}{a}_{n-1}} +\frac{1}{{a}_{3}{a}_{n-2}} +.....+\frac{1}{{a}_{n}{a}_{1}} =...
- 1,319
9
votes
8
answers
3k
views
The sum of consecutive integers is $50$. How many integers are there?
I started off by calling the number of numbers in my list "$n$". Since the integers are consecutive, I had $x + (x+1) + (x+2)...$ and so on. And since there were "$n$" numbers in my list, the last ...
-1
votes
4
answers
2k
views
How to find first 15 terms of an arithmetic progression? [closed]
I am stuck on this AP questions. I know I need to find the difference, first time and such. But I am not sure how.
The sum of the first 15 terms of an Arithmetic Progression is 100 and its 10th term ...
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