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Recent questions tagged summation

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32
summation
5 digit numbers are possible from digits 1, 2, 3, 4, 5, 6, 7 When each digit is distinct is 7P5 . what is sum of all such numbers?
5 digit numbers are possible from digits 1, 2, 3, 4, 5, 6, 7 When each digit is distinct is 7P5 . what is sum of all such numbers?
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18 votes
3 answers
33
ISRO2016-2
What is the sum to infinity of the series, $3+6x^{2}+9x^{4}+12x^{6}+ \dots$ given $\left | x \right |<1$ $\frac{3}{(1+x^{2})}$ $\frac{3}{(1+x^{2})^{2}}$ $\frac{3}{(1-x^{2})^{2}}$ $\frac{3}{(1-x^{2})}$
What is the sum to infinity of the series,$3+6x^{2}+9x^{4}+12x^{6}+ \dots$ given $\left | x \right |<1$$\frac{3}{(1+x^{2})}$$\frac{3}{(1+x^{2})^{2}}$$\frac{3}{(1-x^{2})^{...
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4 votes
2 answers
34
ISI2013-PCB-A-2
Find the value of $ \Sigma ij$, where the summation is over all integers $i$ and $j$ such that $1 \leq i < j \leq 10$.
Find the value of $ \Sigma ij$, where the summation is over all integers $i$ and $j$ such that $1 \leq i < j \leq 10$.
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1 votes
1 answer
35
Find a formula when m is a positive integer?
$(a) \sum_{k = 0}^{m} \left \lfloor \sqrt k \right \rfloor$ $(b) \sum_{k = 0}^{m} \left \lfloor \sqrt {k^{3}} \right \rfloor$ Is there any quick way to find the formula for complex expression?
$(a) \sum_{k = 0}^{m} \left \lfloor \sqrt k \right \rfloor$$(b) \sum_{k = 0}^{m} \left \lfloor \sqrt {k^{3}} \right \rfloor$Is there any quick way to find the formula for...
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1 votes
1 answer
36
What are the values of the sum?
$\sum_{j \in S} 1$ where S = {1, 3, 5, 7}. if we have $\sum_{j = 1}^{n} 1$ then the answer will be n. But what happens if this a set?
$\sum_{j \in S} 1$ where S = {1, 3, 5, 7}.if we have $\sum_{j = 1}^{n} 1$ then the answer will be n. But what happens if this a set?
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9 votes
1 answer
37
GATE2015 EC-3: GA-9
$\log \tan 1^o + \log \tan 2^o + \dots + \log \tan 89^o$ is $\ldots$ $1$ $1/\sqrt{2}$ $0$ $−1$
$\log \tan 1^o + \log \tan 2^o + \dots + \log \tan 89^o$ is $\ldots$$1$$1/\sqrt{2}$$0$$−1$
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18 votes
2 answers
39
GATE CSE 1994 | Question: 15
Use the patterns given to prove that $\sum\limits_{i=0}^{n-1} (2i+1) = n^2$ (You are not permitted to employ induction) Use the result obtained in (A) to prove that $\sum\limits_{i=1}^{n} i = \frac{n(n+1)}{2}$
Use the patterns given to prove that$\sum\limits_{i=0}^{n-1} (2i+1) = n^2$(You are not permitted to employ induction)Use the result obtained in (A) to prove that $\sum\li...
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17 votes
8 answers
40
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then$P = Q - k$$P = Q...
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