Find the sum of first `n`terms of the following series:`5+11+19+29+41+

1.	Find the sum of first `n`terms of the following series:`5+11+19+29+41+ dot`
Answer» Let `S_(n)=5+11+19+29+...+T_(n-1)+T_(n)` `S_(n)=5+11+19+...+T_(n-2)+T_(n-1)+T_(n)` On substraction, we get `0=5+[6+8+10+12= ..." to "(n-1)" terms"]-T_(n)` `rArr T_(n)=5+((n-1)xx[2xx6+(n-2)xx2])/(2)` `rArr T_(n)=5+(n-1)(n+4)` `rArr T_(n)=n^(2)+3n+1.` `therefore S_(n) =sum_(k=1)^(n)T_(k)=sum_(k=1)^(n)(k^(2)+3k+1)=sum_(k=1)^(n)k^(2)+3sum_(k=1)^(n)k+n` `=(1)/(6)n(n+1)(2n+1)+3xx(1)/(2)n(n+1)+n` `=(1)/(3)n(n+2)(n+4).`

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