Statement 1:The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000. 

Statement  2: \sum_{k=1}^{n}\left ( k^{3} -\left ( k-1 \right )^{3}\right )=n^{3} for any natural number n.

 

  • Option 1)

    Statement 1 is false, statement 2 is true

  • Option 2)

    Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Option 3)

    Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Option 4)

    Statement 1 is true, statement 2 is false

 

Answers (2)

As we learnt in

Sequence -

Arragement of real numbers specified in a definite order, by some assigned law.

- wherein

Notations -

a_{1},a_{2},a_{3},a_{4}.........a_{n}

or

< a_{n}>

 

 

Statement 1 :  1+(1+2+4)+(4+6+9)+....+(361+380+400)\; is\; 8000

Statement 2 :      \sum_{k=1}^{n}(k^{3}-(k-1)^{3})=n^{3}

Statement 1 : T_{1}=1,T_{2}=7=8-1

T_{3}=19=27-8\Rightarrow T_{n}=n^{3}-(n-1)^{3}

\therefore \;  Statement 2 is a correct explanation of statement 1.

 


Option 1)

Statement 1 is false, statement 2 is true

This option is incorrect.

Option 2)

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

This option is correct.

Option 3)

Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

This option is incorrect.

Option 4)

Statement 1 is true, statement 2 is false

This option is incorrect.

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