Maths-
General
Easy
Question
The sum of series
is
- None of these
The correct answer is: ![e to the power of negative 1 end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAARCAYAAAAhUad0AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAI9JREFUeNpjYKAtUAPiWiC+wEBHsBiI04D4P8MAgKFp6X88eHj5lOqWigPxGiD+AcQPgdie1pbyAfElIPaD8rWA+AoN4h8FdAFxJZrYFiBmo1WYMwHxByAWRRP7BKVpAsxxBMVRWqYuUDyuoneStgTikwORl64BcQE0DgWhicqW1pYqAfFhIP4DdUAyw3ACAKsAK0WNEdmTAAAAd3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtaT5lPC9taT48bXJvdz48bW8+LTwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21zdXA+PC9tYXRoPpTCoKAAAAAASUVORK5CYII=)
We have, ![not stretchy sum subscript n equals 1 end subscript superscript infinity end superscript fraction numerator 2 n over denominator open parentheses 2 n plus 1 close parentheses factorial end fraction equals not stretchy sum subscript n equals 1 end subscript superscript infinity end superscript fraction numerator 2 n plus 1 minus 1 over denominator open parentheses 2 n plus 1 close parentheses factorial end fraction](data:image/png;base64,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)
![equals not stretchy sum subscript n equals 1 end subscript superscript infinity end superscript open parentheses fraction numerator 1 over denominator open parentheses 2 n close parentheses factorial end fraction minus fraction numerator 1 over denominator open parentheses 2 n plus 1 close parentheses factorial end fraction close parentheses](data:image/png;base64,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)
![not stretchy sum subscript n equals 1 end subscript superscript infinity end superscript fraction numerator 1 over denominator open parentheses 2 n close parentheses factorial end fraction minus not stretchy sum subscript n equals 1 end subscript superscript infinity end superscript fraction numerator 1 over denominator open parentheses 2 n plus 1 close parentheses factorial end fraction](data:image/png;base64,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)
![equals open square brackets fraction numerator e plus e to the power of negative 1 end exponent over denominator 2 end fraction minus 1 close square brackets minus open square brackets fraction numerator e minus e to the power of negative 1 end exponent over denominator 2 end fraction minus 1 close square brackets equals e to the power of negative 1 end exponent](data:image/png;base64,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)
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intersect the line
at P and Q respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R
Statement - 1 : The ratio PR : RQ equals ![2 square root of 2 colon square root of 5](data:image/png;base64,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)
Statement - 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.
The line
and
intersect the line
at P and Q respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R
Statement - 1 : The ratio PR : RQ equals ![2 square root of 2 colon square root of 5](data:image/png;base64,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)
Statement - 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.
maths-General
maths-
If one of the lines given by
is 3x + 4y = 0, then c equals :
If one of the lines given by
is 3x + 4y = 0, then c equals :
maths-General
maths-
If the sum of first
natural numbers is 1/5 times the sum of their squares, then the value of
is
If the sum of first
natural numbers is 1/5 times the sum of their squares, then the value of
is
maths-General
maths-
If
, then the value of x in terms of y is
If
, then the value of x in terms of y is
maths-General
maths-
Given the lines y + 2x = 3 and y + 2x = 5 cut the axes at A, B and C, D respectively.
Statement- I ABDC forms quadrilateral and point (2, 3) lies inside the quadrilateral
Statement- II Point lies on same side of the lines.
Given the lines y + 2x = 3 and y + 2x = 5 cut the axes at A, B and C, D respectively.
Statement- I ABDC forms quadrilateral and point (2, 3) lies inside the quadrilateral
Statement- II Point lies on same side of the lines.
maths-General
Maths-
The x-coordinates of the vertices of a square of unit area are the roots of the equation
and the y-coordinates of the vertices are the roots of the equation
then the possible vertices of the square is/are :
therefore the possible vertices of the square are (1,1),(1,2),(2,1),(2,2) and (−1,1),(−1,2),(−2,2),(−2,1)
The x-coordinates of the vertices of a square of unit area are the roots of the equation
and the y-coordinates of the vertices are the roots of the equation
then the possible vertices of the square is/are :
Maths-General
therefore the possible vertices of the square are (1,1),(1,2),(2,1),(2,2) and (−1,1),(−1,2),(−2,2),(−2,1)
Maths-
The straight lines x + y = 0, 3x + y - 4 = 0 and x + 3y -4 = 0 form a triangle which is
therefore it forms an isosceles triangle
The straight lines x + y = 0, 3x + y - 4 = 0 and x + 3y -4 = 0 form a triangle which is
Maths-General
therefore it forms an isosceles triangle
Maths-
Equation of a straight line passing through the point (4, 5) and equally inclined to the lines 3x = 4y + 7 and 5y = 12x + 6 is
Equation of a straight line passing through the point (4, 5) and equally inclined to the lines 3x = 4y + 7 and 5y = 12x + 6 is
Maths-General
Maths-
If the equation
represents a pair of lines whose slopes are m and
, then value(s) of a is/are -
If the equation
represents a pair of lines whose slopes are m and
, then value(s) of a is/are -
Maths-General
maths-
The curve passing through the points of intersection of
and
represents a pair of straight lines which are
The curve passing through the points of intersection of
and
represents a pair of straight lines which are
maths-General
maths-
The number of divisors of
and
are in
The number of divisors of
and
are in
maths-General