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Find the sum of 'n' terms of 1.2 +2.3+3....

Find the sum of 'n' terms of 1.2 +2.3+3.4+4.5+……

Text Solution

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`T_(n)=` (nth term of 1,2,3,…….)(nth term of 2,3,4..)
`=n(n+1)=n^(2)+n`
`thereforeS_(n)=sumT_(n)=sumn^(2)sum+n`
`=(n(n+1)(2n+1))/(6)+(n(n+1))/(2)=(n(n+1))/(2)[(2n+1)/(3)+1]`
`=(n(n+1)(2n+4))/(6)=(n(n+1)(n+2))/(3)`
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