By induction,it can be proved $4^{3} + 8^{3} + 12^{3} +$ _____ upto n terms $= 16 n^{2} (n + 1)^{2}$ .

True

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False

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Solution

The correct option is A True

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Similar questions

4^{3} + 8^{3} + 12^{3} + . . . + n

1^{2} + 3^{2} + 5^{2} . . . {(2 n - 1)}^{2} = \frac{n (2 n - 1) (2 n + 1)}{3} \forall n \in N

p (n) = {1^{3} + 2^{3} + 3^{3} + . . . . + n^{3} = \frac{n^{2} {(n + 1)}^{2}}{4}}

1^{2} + (1^{2} + 2^{2}) + (1^{2} + 2^{2} + 3^{2}) + \dots

n

= \frac{n {(n + 1)}^{2} (n + 2)}{12}

\frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + . . . . .

n

= \frac{n}{n + 1}

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