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Statement 1 The sum of the series 1+(1+...

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)(k^(3)-(k-1)^(3))=n^(3)` for any natural number n.

A

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

B

Statement 1 is true , Statement 2 is false

C

Statement 1 is false, Statement 2 is ture.

D

Statement 1 is true, Statement 2 is true , Statement 2 is a correct explanation for Statement 1.

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The correct Answer is:
D
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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(k^3-(k-1)^3)=n^3for any natural number n. (1) Statement-1 is true, Statement-2 is false. (2) Statement-1 is false, Statement-2 is true. (3) Statement-1 is true, Statement-2 is true Statement-2 is a correct explanation for Statement-l (4) Statement-1 is true, Statement-2 is true Statement-2 is not a correct explanation for Statement-l.

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MOTION-SEQUENCE & SERIES -Exercise -4 Level -I Previous Year /JEE Main
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  3. the sum of the series 1/(2!)-1/(3!)+1/(4!)-....... upto infinity is

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  4. 1+2/3+6/(3^2)+10/(3^3)+14/(3^4)+

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  5. A person is to count 4500 currency notes. Let an denote the number o...

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  6. Statement 1 The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+"……."+(...

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  7. If 100 times the 100^(t h) term of an AP with non zero common diffe...

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  8. The sum of first 20 terms of the sequence 0.7, 0.77, 0.777...... is

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  13. The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)...

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  14. If m is the AM of two distinct real numbers l and n (l,ngt1) and G(1)...

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  15. If the 2^(nd), 56^(th) and 9^(th) terms of a non-constant A. P. are in...

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  16. If the sum of the first ten terms of the series (1 3/5)^2+(2 2/5)^2+(3...

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  17. For any three positive real numbers a, b and c, 9(25a^2+b^2)+25(c^2-3a...

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  18. Let A be the sum of the first 20 terms and B be the sum of the first 4...

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