STATEMENT 1:- The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+........+(361+380+400) is 8000. STATEMENT 2:- Sigma(k=1 to k=n) [k^3 - (k-1)^3] = n^3, for any natural number n. A) 1 is false, 2 is true. B) 1 is true, 2 is true; 2 is a correct explanation of 1. C) 1 is true, 2 is true; 2 is not a correct explanation of 1. D) 1 is true, 2 is false. Explain in detail.

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Solution

Statement 1 is true and statement 2 is true

2 is not the correct explanation for 1

Try it put k=1 in statement 1
we get 1 which is the first term in statement 1

put k=2 we get 8-1=7
Same as 1+2+4
But 7 not equal to 2^3(n^3)

Put k=3 we get 64-27=37
same as 9+12+16=37
But 37 not equal to = 3^3 (n^3)

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Similar questions

\sum_{k = 1}^{n} (k^{3} - (k - 1)^{3}) = n^{3},

\sum_{k = 1}^{n} (k^{3} - (k - 1)^{3}) = n^{3},

\sum_{k = 1}^{n} (k^{3} - (k - 1)^{3}) = n^{3},

n \geq 2,

\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + . . . + \frac{1}{\sqrt{n}} > \sqrt{n}

\sqrt{n (n + 1)} < n + 1

1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + \dots + (361 + 380 + 400)

8000.

n \sum k = 1 (k^{3} - (k - 1)^{3}) = n^{3}

n

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