Math Solution-2

Hello, guys here is the set of solutions ,to yesterday's questions

1) 5/2+9/4+17/8+33/16+.... to n terms

   = 2+ 1/2 + 2 + 1/4 + 2 + 1/8 + 2+ 1/16 + ...

   = (2+2+2+....n terms) + (1/2+1/4+1/8+....n terms)
 
   =  2n + 1/2 (1-1/2^n)/(1-1/2)
 
   = 2n+1 -1/2^n


short cut :-
                substitue 1 in option one and see if it is 5/2
                similarly substitue 2 and add 5/2 and 9/4
                if it matches then it is d correct option else go to option two.


2) let the 1st term and the common difference (c.d) be a and d
 

    now, [(a+(2-1)d) + (a + (9-1)d)+ (a+ (18-1)d)] {since nth term in A.P is a + (n-1)d}

         = [(a+7d)+ (a+15d)] ,{given that sum of 2nd 9th 18th is equal to sum of 8th and 16th }

       => 3a + 26d = 2a + 22d

       => a + 4d = 0
 
     Hence 5th term is zero.


3) Here 777k + 65 is the number. 777 is divisible by 37
 
    Therefore reminder when divided by 37 is same as the reminder when divied by
    37. therefore the reminder is rem(65/37) which is 28.




4) (A/(x-1)) + (B/(x+2))=1

   when  A = 0 ,

    B/(x+2)= 1

   => x= B-2
 
   => only one root


   when B=0,
 
   A/(x+2) =1
 
   => x=A+1

   =>only one root

  when both are not equal to zero

 we get 2 distinct roots.

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