Sequences and Series


   
 
General Series
1. To find the sum of first n natural numbers.
 
or
 
 
Suggested answer:
 
Let Sn = 1+2+3+4+...+n
 
This series is an A.P.
 
Here a=1, d=1, l = tn = n
 
 
     
 
 
2. To find the sum to squares of first n natural numbers.
 
or
 
 
Suggested answer:
 
 
 
 
 
 
. . . .
 
. . . .
 
. . . .
 
 
 
Adding vertically,
 
 
 
 
 
 
3. To find the sum to the cubes of first n natural numbers.
 
or
 
 
Suggested answer:
 
 
 
 
 
 
 
 
Adding vertically,
 
 
 
 
 
4. Method of finding sum of a series whose nth term is known.
 
Suggested answer:
 
Let the nth term of series be an3 + bn2 + cn + d
 
tn = an3 + bn2 + cn + d where a, b, c, d are constants.
 
 
                  
 
 
     
   
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