Question

The sum of series $fraction numerator 1 over denominator 2 space factorial end fraction space plus fraction numerator 1 over denominator 4 factorial end fraction space plus fraction numerator 1 over denominator 6 space factorial end fraction space plus space.... space is$

$fraction numerator left parenthesis straight e squared minus 1 right parenthesis over denominator 2 end fraction$
$fraction numerator left parenthesis straight e minus 1 right parenthesis squared over denominator 2 straight e end fraction$
$fraction numerator left parenthesis straight e squared minus 1 right parenthesis over denominator 2 straight e end fraction$
$fraction numerator left parenthesis straight e minus 1 right parenthesis squared over denominator straight e end fraction$

Solution

fraction numerator left parenthesis straight e minus 1 right parenthesis squared over denominator 2 straight e end fraction

straight e space equals space 1 space plus space fraction numerator 1 over denominator 1 factorial end fraction space plus fraction numerator 1 over denominator 2 factorial end fraction space plus fraction numerator 1 over denominator 3 factorial end fraction space plus space fraction numerator 1 over denominator 4 factorial end fraction space plus space....... infinity space.... space left parenthesis straight i right parenthesis straight e to the power of negative 1 end exponent space equals 1 space minus space fraction numerator 1 over denominator 1 factorial end fraction space plus fraction numerator 1 over denominator 2 factorial end fraction space minus fraction numerator 1 over denominator 3 factorial end fraction space plus space fraction numerator 1 over denominator 4 factorial end fraction space minus space....... infinity space.... space left parenthesis ii right parenthesis on space adding space equ space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis straight e space plus straight e to the power of negative 1 end exponent space space equals space 2 space plus space fraction numerator 2 over denominator 2 space factorial end fraction space plus fraction numerator 2 over denominator 4 factorial end fraction space plus........ space infinity fraction numerator straight e squared plus 1 over denominator straight e end fraction minus 2 space equals space fraction numerator 2 over denominator 2 factorial end fraction space plus fraction numerator 2 over denominator 4 factorial end fraction space plus....... infinity fraction numerator straight e squared space plus 1 minus 2 straight e over denominator straight e end fraction space equals space 2 space open square brackets fraction numerator 1 over denominator 2 factorial end fraction fraction numerator 1 over denominator 4 space factorial end fraction space plus..... infinity close square brackets fraction numerator left parenthesis straight e minus 1 right parenthesis squared over denominator 2 straight e end fraction space equals space fraction numerator 1 over denominator 2 factorial end fraction space plus fraction numerator 1 over denominator 4 factorial end fraction space plus space...... infinity

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Sequences And Series

Some More Questions From Sequences and Series Chapter

Coordinate planes divide the space into _______ octants.

Let P (-2, 3, -4) is a point in space. Find the co-ordinates of the foot of perpendicular from this point to ZX-plane.

Let P (-2, 3, -4) is a point in space. Find the foot of perpendicular from this point to the z-axis.

Let P (-2, 3, -4) is a point in space. Find the the perpendicular distance of P from XY-plane.

Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

Find the octant in which the following points lie:
A (-3,1, 2), B (-3, 1, -2), C (-3, -1,-2), D (3, -1, -2) and E (3,1, 2).

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Sequences And Series

The sum of series

Some More Questions From Sequences and Series Chapter

Coordinate planes divide the space into _______ octants.

Let P (-2, 3, -4) is a point in space. Find the co-ordinates of the foot of perpendicular from this point to ZX-plane.

Let P (-2, 3, -4) is a point in space. Find the foot of perpendicular from this point to the z-axis.

Let P (-2, 3, -4) is a point in space. Find the the perpendicular distance of P from XY-plane.

Name the octants in which the following points lie:A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

Find the octant in which the following points lie:A (-3,1, 2), B (-3, 1, -2), C (-3, -1,-2), D (3, -1, -2) and E (3,1, 2).

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

Find the octant in which the following points lie:
A (-3,1, 2), B (-3, 1, -2), C (-3, -1,-2), D (3, -1, -2) and E (3,1, 2).