1
AIEEE 2004
+4
-1
Out of Syllabus
The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + ....\,is\,{{n{{(n + 1)}^2}} \over 2}$$ when n is even. When n is odd the sum is
A
$${\left[ {{{n(n + 1)} \over 2}} \right]^2}$$
B
$${{{n^2}(n + 1)} \over 2}$$
C
$${{n{{(n + 1)}^2}} \over 4}$$
D
$$\,{{3n(n + 1)} \over 2}$$
2
AIEEE 2004
+4
-1
Out of Syllabus
The sum of series $${1 \over {2\,!}} + {1 \over {4\,!}} + {1 \over {6\,!}} + ........$$ is
A
$${{\left( {{e^2} - 2} \right)} \over e}\,$$
B
$${{{{\left( {e - 1} \right)}^2}} \over {2e}}$$
C
$${{\left( {{e^2} - 1} \right)} \over {2e}}\,$$
D
$${{\left( {{e^2} - 1} \right)} \over 2}$$
3
AIEEE 2003
+4
-1
Out of Syllabus
The sum of the serier $${1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}}..............$$ up to $$\infty$$ is equal to
A
$$\log {\,_e}\left( {{4 \over e}} \right)\,\,$$
B
$$2\,\log {\,_e}2$$
C
$$\log {\,_e}2 - 1\,$$
D
$$\log {\,_e}2$$
4
AIEEE 2002
+4
-1
If 1, $${\log _9}\,\,({3^{1 - x}} + 2),\,\,{\log _3}\,\,({4.3^x} - 1)$$ are in A.P. then x equals
A
$${\log _3}\,4\,\,\,$$
B
$$1 - \,{\log _3}\,4\,$$
C
$$1 - \,{\log _4}\,3$$
D
$${\log _4}\,3$$
EXAM MAP
Medical
NEET