AIEEE 2004 | Sequences and Series Question 268 | Mathematics

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

$${\left[ {{{n(n + 1)} \over 2}} \right]^2}$$

$${{{n^2}(n + 1)} \over 2}$$

$${{n{{(n + 1)}^2}} \over 4}$$

$$\,{{3n(n + 1)} \over 2}$$

AIEEE 2004

MCQ (Single Correct Answer)

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Out of Syllabus

The sum of series $${1 \over {2\,!}} + {1 \over {4\,!}} + {1 \over {6\,!}} + ........$$ is

$${{\left( {{e^2} - 2} \right)} \over e}\,$$

$${{{{\left( {e - 1} \right)}^2}} \over {2e}}$$

$${{\left( {{e^2} - 1} \right)} \over {2e}}\,$$

$${{\left( {{e^2} - 1} \right)} \over 2}$$

AIEEE 2003

MCQ (Single Correct Answer)

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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

$$\log {\,_e}\left( {{4 \over e}} \right)\,\,$$

$$2\,\log {\,_e}2$$

$$\log {\,_e}2 - 1\,$$

$$\log {\,_e}2$$

AIEEE 2002

MCQ (Single Correct Answer)

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l, m, n are the $${p^{th}}$$, $${q^{th}}$$ and $${r^{th}}$$ term of a G.P all positive, $$then\,\left| {\matrix{ {\log \,l} & p & 1 \cr {\log \,m} & q & 1 \cr {\log \,n} & r & 1 \cr } } \right|\,equals$$

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