JEE Mathematics/ Lakshmikanta Satapathy/ Sequences and Series QA part 3/ JEE question on the sum of a special sequence solved with the related concepts

1. Physics Helpline
L K Satapathy
Sequences & Series 3

2. Physics Helpline
L K Satapathy
Sequence and Series 3
Question : If the sum of the first ten terms of the series
, then the value of m is
Answer :
( ) 102 ( ) 101 ( ) 100 ( ) 99a b c d
       
2 2 2 2
23 2 1 4 161 2 3 4 4 . . .
5 5 5 5 5
is m    
       
2 2 2 2
23 2 1 41 2 3 4 4 . . .
5 5 5 5
Let S       Upto 10 terms
         
2 2 2 2 2
8 12 16 20 24 . . .
5 5 5 5 5
S       Upto 10 terms
         
2 2 2 2 21 8 12 16 20 24 . . .
25
      
 
Upto 10 terms

3. Physics Helpline
L K Satapathy
Sequence and Series 3
Correct option = (b)
Upto 10 terms2 2 2 2
' 8 12 16 20 . .Let S     
 
2
4( 1)nT n   Where n varies from 1 to 10
 
10 10 10 10 10
2 2 2
1 1 1 1 1
' 4( 1) 16 ( 2 1) 16 2 1
n n n n n
S n n n n n
    
 
         
 
    
10 11 21 10 1116 2 10
6 2
      
  
 16 385 110 10 16 505    
' 1 16 116 505 16 505
25 25 5 25
S mS        
101 [ ]m Ans 
2 ( 1)(2 1)
6
n n n
n
  
  


4. Physics Helpline
L K Satapathy
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