Maths-
General
Easy
Question
Let
is an even integer. If
is assumed true
is true. Therefore
is true :
- for
- for all
- for
- for no
Hint:
Mathematical reasoning or the principle of mathematical reasoning is a part of mathematics where we determine the truth values of the given statements.
The correct answer is: for no ![n element of N](data:image/png;base64,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)
Given :
is an even integer
Let this be true for n = k
P(k)
is an even integer
This is also true for P(k +1)
P(k +1) = ![open parentheses k space plus space 1 close parentheses squared space plus space left parenthesis k plus 1 right parenthesis space plus space 1](data:image/png;base64,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)
P(k +1) = ![k squared space plus space 1 space plus 2 k space plus space left parenthesis k plus 1 right parenthesis space plus space 1](data:image/png;base64,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)
P(k +1) = ![k squared space plus space k space plus space 1 space plus space 2 k space plus 2](data:image/png;base64,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)
![w e space k n o w space t h a t space space k squared space plus space k space plus space 1 space i s space a n space e v e n space i n t e g e r](data:image/png;base64,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)
![P left parenthesis k space plus 1 right parenthesis space space equals space e v e n space plus space 2 left parenthesis K space plus 1 right parenthesis
2 left parenthesis k space plus 1 right parenthesis space w i l l space a l s o space b e space e v e n
P left parenthesis k plus 1 right parenthesis space equals space e v e n space plus space e v e n space equals space e v e n space i n t e g e 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P left parenthesis n right parenthesis space equals space n left parenthesis n plus 1 right parenthesis space plus space 1 comma
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)
Related Questions to study
maths-
If
is a statement
such that if
is true,
is true for
, then
is true.
If
is a statement
such that if
is true,
is true for
, then
is true.
maths-General
physics
The resultant of two vectors is maximum when they
The resultant of two vectors is maximum when they
physicsGeneral
physics
and A=B=C Find the angle between
and ![Error converting from MathML to accessible text.](data:image/png;base64,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)
and A=B=C Find the angle between
and ![Error converting from MathML to accessible text.](data:image/png;base64,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)
physicsGeneral
physics
A and
are nonzero vectors. Which from the followings is true?
A and
are nonzero vectors. Which from the followings is true?
physicsGeneral
physics
1+2j+2k, calculate the angle between
and Y axis
1+2j+2k, calculate the angle between
and Y axis
physicsGeneral
physics
and
are in opposite direction so they are
and
are in opposite direction so they are
physicsGeneral
physics
=
is true, if
=
is true, if
physicsGeneral
physics
and
are equal vectors what from the followings is true
and
are equal vectors what from the followings is true
physicsGeneral
physics
Which from the following is a scalar ?
Which from the following is a scalar ?
physicsGeneral
maths-
The greatest positive integer which divide
is
The greatest positive integer which divide
is
maths-General
maths-
The sets
are given by
then the sum of numbers in the set
is :
The sets
are given by
then the sum of numbers in the set
is :
maths-General
maths-
If ![S subscript 1 equals left curly bracket 1 right curly bracket comma S subscript 2 equals left curly bracket 2 comma 4 right curly bracket comma S subscript 3 equals left curly bracket 3 comma 6 comma 9 right curly bracket S subscript 4 equals left curly bracket 4 comma 8 comma 12 comma 16 right curly bracket comma horizontal ellipsis horizontal ellipsis](data:image/png;base64,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)
then sum of the numbers in the set is
If ![S subscript 1 equals left curly bracket 1 right curly bracket comma S subscript 2 equals left curly bracket 2 comma 4 right curly bracket comma S subscript 3 equals left curly bracket 3 comma 6 comma 9 right curly bracket S subscript 4 equals left curly bracket 4 comma 8 comma 12 comma 16 right curly bracket comma horizontal ellipsis horizontal ellipsis](data:image/png;base64,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)
then sum of the numbers in the set is
maths-General
maths-
If
is even,
terms
, if
is odd then ![S subscript n equals](data:image/png;base64,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)
If
is even,
terms
, if
is odd then ![S subscript n equals](data:image/png;base64,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)
maths-General
biology
Central Rice Research Institute (CRRI) is situated at
Central Rice Research Institute (CRRI) is situated at
biologyGeneral
physics
In the above figure
and
are two vectors. What from followings is true
![](data:image/png;base64,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)
In the above figure
and
are two vectors. What from followings is true
![](data:image/png;base64,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)
physicsGeneral