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Recent questions tagged exercise9-4

Find the sum of $n$ terms of the series whose $n^{th}$ term is $(2n-1)^2$

asked Mar 27, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series whose $n^{th}$ term is given by $n^2+2^n$.

asked Mar 24, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series whose $n^{th}$ term is given by $n(n+1)(n+4)$

asked Mar 24, 2014 by rvidyagovindarajan_1

1 answer

Find the sum to $n$ terms of the series $1^2+(1^2+2^2)+(1^2+2^2+3^2)+........$

asked Mar 24, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $(3\times 8)+(6\times 11)+(9\times 14).............$

asked Mar 13, 2014 by rvidyagovindarajan_1

1 answer

Find the sum to $n$ terms of the series $\large\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+..........$

asked Mar 10, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $3\times 1^2+5\times 2^2+7\times 3^2+.........$

asked Mar 7, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $(1\times 2\times 3)+(2\times 3\times 4)+(3\times 4\times 5)+.......$

asked Mar 7, 2014 by rvidyagovindarajan_1

1 answer

Find the sum of $n$ terms of the series $1\times 2+2\times 3+3\times 4+4\times 5+.............$

asked Mar 7, 2014 by rvidyagovindarajan_1

1 answer

A lot of 100 watches is known to have 10 defective watches.If 8 watches are selected(one by one with replacement) at random,what is the probability that there will be at least one defective watch?

asked Jan 9, 2013 by sreemathi.v

1 answer

Show that the set $ G = \{2^n / n \in Z\} $ is an abelian group under multiplication.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set of all matrices of the form $\bigl(\begin{smallmatrix} a & 0 \\ 0 & 0 \end{smallmatrix} \bigr) $, $a \in R$ − {0} forms an abelian group under matrix multiplication.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the order of each element in the group $ (Z_5 − \{[0]\}, _.5)$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set {[1], [3], [4], [5], [9]} forms an abelian group under multiplication modulo 11.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set G of all rational numbers except − 1 forms an abelian group with respect to the operation $$ given by $a b = a + b + ab$ for all $a, b \in G$.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set M of complex numbers z with the condition | z | = 1 forms a group with respect to the operation of multiplication of complex numbers.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that { $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega & 0 \\ 0 & \omega^2\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega^2 & 0 \\ 0 & \omega\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega^2\\ \omega & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega\\ \omega^2 & 0\end{smallmatrix} \bigr) $} where $\omega^3 = 1, \omega \neq 1$ form a group with respect to matrix multiplication.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set G of all positive rationals forms a group under the composition $$ defined by $a b = (\large\frac{ab}{3})$ for all $a, b \in G.$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Prove that the matrices $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix} \bigr) $ form a group under matrix multiplication

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set of all positive even integers forms a semi-group under the usual addition and multiplication. Is it a monoid under each of the above operations?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set N of natural members is a semi-group under the operation $x * y $= max {x, y}. Is it a monoid?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let $S$ be a non-empty set and o be a binary operation on $S$ defined by $xoy = x ; x, y \in S$. Determine whether o is commutative and associative.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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