Direction: (Q. Nos. 89) For the following questions, the correct answers from the codes (a), (b), (c) and (d) defined as follows. |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I.
B) Statement I is true, Statement II is also true and Statement II is not the correct explanation of Statement I.
C) Statement I is true, Statement II is false.
D) Statement I is false, Statement II is true.
Correct Answer: A
Solution :
\[{{T}_{1}}=1,\] \[{{T}_{2}}=7=(8-1)\] \[{{T}_{3}}=19=(27-8)\] ?????????? ?????????? \[{{T}_{n}}={{n}^{3}}-{{(n-1)}^{3}}\] \[\therefore \] \[{{S}_{n}}=\Sigma \,\,{{T}_{n}}=({{n}^{3}}-{{n}^{3}}+1-3n+3{{n}^{2}})\] \[=\Sigma \,\left( 3{{n}^{2}}-3n+1 \right)\] \[=\frac{3n(n+1)\,(2n+1)}{6}\,-\frac{3n\,(n+1)}{2}+n\] \[=\frac{3n\,(n+1)}{6}\,(2n+1-3)+n\] \[=n(n+1)\,(n-1)+n\] \[=n[{{n}^{2}}-1+1]={{n}^{3}}\] \[\therefore \] \[{{S}_{20}}={{(20)}^{3}}=8000\]You need to login to perform this action.
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