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  • Sum to 30 terms of the series 1/1.2.3 +1/ 2. 3. 4 +1/ 3.4.5+........ is

Sum to 30 terms of the series 1/1.2.3 +1/ 2. 3. 4 +1/ 3.4.5+........ is

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Solution:   We have,    1/1cdot 2cdot 3+1/2cdot 3cdot4+1/3cdot 4cdot 5+...............

                 T_r=1/r(r+1)(r+2)=1/2r -1/r+1+1/2(r+2)

                T_r=1/2[1/r-1/r+1]-1/2[1/r+1-1/r+2]

           Rightarrow       S_n=sum_r=1^nT_r=1/2[1-1/n+1]-1/2[1/2-1/n+2]=(1/2)[n/n+1]-[n/4(n+2)]

           Rightarrow     S_30=(1/2)(30/31)-(30/4cdot 32)=(30/4)[60-31/(31)(32)]=495/1984

           

Posted by

Deependra Verma

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