Find the sum to n terms of the series :- 5 + 11 + 19 + 29 + 41 +..........
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5+11+19+29+41.........
(2^2+1)+(3^2+2)+(4^2+3)+(5^2+4).........
tr= (r+1)^2+r
=r^2+3r+1
now use concept of sigma
sigma tr=sigma. r^2+ 3sigma .r+sigma. 1
=n (n+1)(2n+1)/6+3n (n+1)/2+n
(2^2+1)+(3^2+2)+(4^2+3)+(5^2+4).........
tr= (r+1)^2+r
=r^2+3r+1
now use concept of sigma
sigma tr=sigma. r^2+ 3sigma .r+sigma. 1
=n (n+1)(2n+1)/6+3n (n+1)/2+n
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