Short Answer Type
Long Answer Type
 Also, show that 
Short Answer TypeLong Answer TypeFind the sum to n terms of the series:
1 . 2 . 4 + 2. 3 . 7 + 3. 4. 10 +..............
Let Tn be the nth terms of the series
    Tn = [nth terms of 1, 2, 3, .......] 
 [ nth terms of 2, 3, 4, ......] 
 [nth term of 4, 7, 10, ........]
Â
     = [ 1 + (n -1) 1] [2 + (n - 1)1] [4 + (n - 1)3]
     = (1 + n - 1) (2 + n - 1) (4 + 3n - 3) = n(n + 1) (3n + 1)
   Tn = 3n3 + 4n2 + n
Let  Sn denote the sum of n terms of the series:
 ∴   
            
 = 
=Â 
=Â 
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 and deduce the sum to infinity.
