What is the sum of n terms of the series $- 1 + 1^{2} - 2 + 2^{2} - 3 + 3^{2}$ … ?

$\frac{n (n^{2} + 1)}{3}$

$n^{2} + n$

$\frac{n (n^{2} - 1)}{3}$

none of these

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The correct Answer is:D

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Updated on:21/07/2023

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Question 1 - Select One
The sum of n terms of the series
$1^{2} + (1^{2} + 3^{2}) + (1^{2} + 3^{2} + 5^{2}) + \dots$ is :
A $\frac{1}{3} (n^{4} + 2 n^{2})$
B $\frac{1}{3} (n^{3} + 3 n^{2} - n)$
C $\frac{1}{6} n (n + 1) (2 n^{2} + 2 n - 1)$
Dnone of these
Question 1 - Select One
The sum of n terms of the series
$1^{2} + (1^{2} + 3^{2}) + (1^{2} + 3^{2} + 5^{2}) + \dots$ is :
A $\frac{1}{3} (n^{3} + n^{2} + 1)$
B $\frac{1}{6} n (n + 1) (2 n^{2} + 2 n - 1)$
C $\frac{1}{3} (2 n^{2} + 2 n - 1)$
Dnone of these
Question 1 - Select One or More
Sum of $n$ terms the series : $1^{2} - 2^{2} + 3^{2} - 4^{2} + 5^{2} - 6^{2} +$
A $- \frac{n}{2} (n + 1)$
B $\frac{n}{2} (n + 1)$
C $- n (n + 1)$
Dnone of these
Question 1 - Select One
The sum of terms of the series $1^{2} + 3^{2} + 5^{2} + \dots$ to n terms us
A $4 n^{2} - 1$
B $4 n^{2} + 1$
C $\frac{n}{3} (4 n^{2} - 1)$
D $\frac{n}{3} (4 n^{2} + 1)$
Question 1 - Select One
The sum of n terms of the series
$\frac{3}{1^{2} \cdot 2^{2}} + \frac{5}{2^{2} \cdot 3^{2}} + \frac{7}{3^{2} \cdot 4^{2}}$ + … is :
A $\frac{n^{2} - 2 n}{{(n - 1)}^{2}}$
B $\frac{n^{2} - 2 n}{{(n + 1)}^{2}}$
C $\frac{2 n^{2} + 1}{n}$
Dnone of these
Question 1 - Select One
The sum of $n$ terms of the series $1^{2} + {2.2}^{2} + 3^{2} + {2.4}^{2} + 5^{2} + {2.6}^{2} + ... .$ is $\frac{n {(n + 1)}^{2}}{2}$ when n is even . when n is odd , the sum is
A $\frac{n^{2} (n + 1)}{2}$
B $\frac{n (n^{2} - 1)}{2}$
C $2 {(n + 1)}^{2} (2 n + 1)$
Dnone

What is the sum of n terms of the series $- 1 + 1^{2} - 2 + 2^{2} - 3 + 3^{2}$ … ?

The correct Answer is:D

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Knowledge Check

The sum of n terms of the series
$1^{2} + (1^{2} + 3^{2}) + (1^{2} + 3^{2} + 5^{2}) + \dots$ is :

The sum of n terms of the series
$1^{2} + (1^{2} + 3^{2}) + (1^{2} + 3^{2} + 5^{2}) + \dots$ is :

Sum of $n$ terms the series : $1^{2} - 2^{2} + 3^{2} - 4^{2} + 5^{2} - 6^{2} +$

The sum of terms of the series $1^{2} + 3^{2} + 5^{2} + \dots$ to n terms us

The sum of n terms of the series
$\frac{3}{1^{2} \cdot 2^{2}} + \frac{5}{2^{2} \cdot 3^{2}} + \frac{7}{3^{2} \cdot 4^{2}}$ + … is :

The sum of $n$ terms of the series $1^{2} + {2.2}^{2} + 3^{2} + {2.4}^{2} + 5^{2} + {2.6}^{2} + ... .$ is $\frac{n {(n + 1)}^{2}}{2}$ when n is even . when n is odd , the sum is

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ARIHANT SSC-SEQUENCE, SERIES & PROGRESSIONS-EXERCISE LEVEL-2

What is the sum of n terms of the series −1+12−2+22−3+32 … ?

The correct Answer is:D

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The sum of n terms of the series 12+(12+32)+(12+32+52)+… is :

The sum of n terms of the series 12+(12+32)+(12+32+52)+… is :

Sum of n terms the series : 12−22+32−42+52−62+

The sum of terms of the series 12+32+52+… to n terms us

The sum of n terms of the series 312⋅22+522⋅32+732⋅42 + … is :

The sum of n terms of the series 12+2.22+32+2.42+52+2.62+.... isn(n+1)22 when n is even . when n is odd , the sum is

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ARIHANT SSC-SEQUENCE, SERIES & PROGRESSIONS-EXERCISE LEVEL-2

What is the sum of n terms of the series $- 1 + 1^{2} - 2 + 2^{2} - 3 + 3^{2}$ … ?

The sum of n terms of the series
$1^{2} + (1^{2} + 3^{2}) + (1^{2} + 3^{2} + 5^{2}) + \dots$ is :

The sum of n terms of the series
$1^{2} + (1^{2} + 3^{2}) + (1^{2} + 3^{2} + 5^{2}) + \dots$ is :

Sum of $n$ terms the series : $1^{2} - 2^{2} + 3^{2} - 4^{2} + 5^{2} - 6^{2} +$

The sum of terms of the series $1^{2} + 3^{2} + 5^{2} + \dots$ to n terms us

The sum of n terms of the series
$\frac{3}{1^{2} \cdot 2^{2}} + \frac{5}{2^{2} \cdot 3^{2}} + \frac{7}{3^{2} \cdot 4^{2}}$ + … is :

The sum of $n$ terms of the series $1^{2} + {2.2}^{2} + 3^{2} + {2.4}^{2} + 5^{2} + {2.6}^{2} + ... .$ is $\frac{n {(n + 1)}^{2}}{2}$ when n is even . when n is odd , the sum is