For a series $S = 1 -2 + 3\, -\, 4 … n$ terms,
Statement $-1$ : Sum of series always dependent on the value of $n$ , i.e. whether it is even or odd.
Statement $-2$ : Sum of series is $-\frac {n}{2}$ when value of $n$ is any even integer
For a series $S = 1 -2 + 3\, -\, 4 … n$ terms,
Statement $-1$ : Sum of series always dependent on the value of $n$ , i.e. whether it is even or odd.
Statement $-2$ : Sum of series is $-\frac {n}{2}$ when value of $n$ is any even integer
- A
Statement $-1$ is true, statement $-2$ is true but statement $-1$ is not the correct explanation for statement $-2$
- B
Statement $-1$ is true, statement $-2$ is false
- C
Statement $-1$ is false, statement $-2$ is true
- D
Both statements are true, and statement $-1$ is the true explanation of statement $-2$
Similar Questions
Let ${S_n}$ denotes the sum of $n$ terms of an $A.P.$ If ${S_{2n}} = 3{S_n}$, then ratio $\frac{{{S_{3n}}}}{{{S_n}}} = $
Let ${S_n}$ denotes the sum of $n$ terms of an $A.P.$ If ${S_{2n}} = 3{S_n}$, then ratio $\frac{{{S_{3n}}}}{{{S_n}}} = $
If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =
If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =
The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is $170$ . If there are at least $6$ houses in that row and $a$ is the number of the sixth house, then
The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is $170$ . If there are at least $6$ houses in that row and $a$ is the number of the sixth house, then
- [KVPY 2014]
Let $AP ( a ; d )$ denote the set of all the terms of an infinite arithmetic progression with first term a and common difference $d >0$. If $\operatorname{AP}(1 ; 3) \cap \operatorname{AP}(2 ; 5) \cap \operatorname{AP}(3 ; 7)=\operatorname{AP}( a ; d )$ then $a + d$ equals. . . . .
Let $AP ( a ; d )$ denote the set of all the terms of an infinite arithmetic progression with first term a and common difference $d >0$. If $\operatorname{AP}(1 ; 3) \cap \operatorname{AP}(2 ; 5) \cap \operatorname{AP}(3 ; 7)=\operatorname{AP}( a ; d )$ then $a + d$ equals. . . . .
- [IIT 2019]
If three positive numbers $a, b$ and $c$ are in $A.P.$ such that $abc\, = 8$, then the minimum possible value of $b$ is
If three positive numbers $a, b$ and $c$ are in $A.P.$ such that $abc\, = 8$, then the minimum possible value of $b$ is
- [JEE MAIN 2017]