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Tushar Watts Grade: 12
        

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, a 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

7 years ago

Answers : (1)

Askiitian.Expert Rajat
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

7 years ago
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