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```        Ques1) 1 -2+3 - 4 + 5 - 6 .................... - 2n is equals to
(a) n       (b) n(n+1)/2     (c)  -n(n+1)/2              (d)    none
Ques2) Let a1,a2,a3,..... be in A.P and ap, aq, ar  be in G.P.  Then show that ap / aq = (q-p) / (r - q).
Ques3) If an >1 for all n belonging to N,
log a2 a1 + log a3 a2 + ..........+ log an an-1 + log a1 an has the min value:-
(a) 1    (b) 2        (c)  0   (d) none```
8 years ago

24 Points
```										Hi Tushar
Please post different questions in a different post, i.e., one question per post.

A1}
1 -2+3 - 4 + 5 - 6 .................... - 2n
=
[1 +2+3 + 4 + 5 + 6 .................... + 2n] - 2[2+ 4  + 6 .................... + 2n]
=
2n(2n+1)/2  -  4(1 +2+3 + 4 + 5 + 6 .................... +n)
=
n(2n+1)  -  4n(n+1)/2
=
n[2n+1 - (2n+2)]
=
n[-1]
=
-n

Method 2:
1 -2+3 - 4 + 5 - 6 .................... - 2n
=
(1 -2)+(3 - 4)+(5 - 6)+.............+[(2n-1)- 2n].................................As you can see, these are n pairs of consecutive terms
=
(-1)+(-1)+(-1)+.........n Times
=
-n

Regards
Rajat
```
8 years ago
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