Question


1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
1 -
1
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
+
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
1 -
2
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
+
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
1 -
3
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
+ ... up to n terms = ?
n
n
n

Options:
A .   1 n 2
B .   1 (n - 1) 2
C .   1 n(n - 1) 2
D .  None of these
Answer: Option B

Given sum
= (1 + 1 + 1 + ... to n terms)
-
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
1
+
2
+
3
+ ... to n terms
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
n
n
n
= n -
n
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
1
+ 1
1 -1      +1 -2      +1 -3      + ... Up To N Terms = ?     ...
    [ Ref: nth terms = (n/n) = 1]
2
n
= n -
n + 1
2
=
1
(n - 1)
2

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