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Question

Find the value of i=1 j=1 k=1 12i2j2k.


A

4

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B

8

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C

16

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D

27

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Solution

The correct option is B

8


i=1 j=1 k=1 12i2j2k

Since, one summation operator uses only one variable

So,first find the summation for k=1 12i2j2k keeping i and j constant.

Similarly extend it for other summation part.

= i=1 j=1 12i2j (120+121+122+123+.....)

= i=1 j=1 12i2j [1112] = i=1 j=1 22i2j

= 2i=1 12i [120+121+122+123+.....] = 2i=1 12i (1112)

= 4i=1 12i

= 4 [120+121+122+123+.....]

= 4 × 1112

= 8


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