Question

Find the sum of following series upto terms.
1+9+24+46+.......

Answer 1

nth term: 3.5n² -2.5n 

The first term is 3.5 times the sum of squares, i.e. 
(3.5 / 6) n(n+1)(2n+1) 

The second is: -2.5 times the sum of integers, i.e.: 
(-2.5/2)n(n+1) 

So adding we have: 
(3.5 / 6)n(n+1)(2n+1) + (-2.5/2)n(n+1) 
S(n) = (1/6)(n)(7n²+3n-4) 

This checks out S(1)=1, S(2)=10, S(3)=34 
If you want, to prove the claim, you could use mathematical induction.
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