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If (1^{2}+2^{2}+3^{3}+.....12^{2})=650, then the value of (2^{

Question

If $(1^{2} + 2^{2} + 3^{3} + .....1 2^{2}) = 650$ , then the value of $(2^{2} + 4^{2} + 6^{2} + ....... + 2 4^{2})$ is

1300

2600

2500

42250

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(1^{2} + 2^{2} + 3^{3} + .....1 2^{2}) = 650

, then the value of

(2^{2} + 4^{2} + 6^{2} + ....... + 2 4^{2})

14 mins ago

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14 mins ago

Text solutionVerified

Solve:

Given,

1^{2} + 2^{2} + 3^{2} + \dots + 1 2^{2} = 650

\Rightarrow (2^{2} + 4^{2} + 6^{2} + \dots .2 4^{2})

we have to

find

2^{2} = 1^{2} \cdot 2^{2}

4^{2} = 2^{2} \cdot 2^{2}

6^{2} = 3^{2} \cdot 2^{2}

\Rightarrow (2^{2} + 4^{2} + 6^{2} + \dots .2 4^{2}) = 2^{2} (1^{2} + 2^{2} + 3^{2} + \dots 2 4^{2})

\Rightarrow (2^{2} + 4^{2} + 6^{2} + \dots 2 4^{2}) = 2^{2} \times 650

\Rightarrow 2^{2} + 4^{2} + 6^{2} + \dots 2 4^{2} = 650 \times 4

\Rightarrow 2^{2} + 4^{2} + 6^{2} + \dots 2 4^{2} = 2600

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