Question

The average of square of natural numbers from 1to71

Answer 1

Answer:

24

Step-by-step explanation:

vi mate 10 7949 is this correct answer

Answer 2

The average of square of natural numbers from 1 to 71 is 1716

Given :

The natural numbers from 1 to 71

To find :

The average of square of natural numbers from 1 to 71

Solution :

Step 1 of 2 :

Find the sum of square of natural numbers from 1 to 71

We know that

$\displaystyle \sf{ {1}^{2} + {2}^{2} + . \: . \: . \: . + {n}^{2} = \frac{n(n + 1)(2n + 1)}{6} }$

The sum of square of natural numbers from 1 to 71

$\displaystyle \sf{ = {1}^{2} + {2}^{2} + . \: . \: . \: . + {71}^{2} }$

$\displaystyle \sf{ = \frac{71(71 + 1)(2 \times 71 + 1)}{6} }$

$\displaystyle \sf{ = \frac{71 \times 72 \times 143}{6} }$

$\sf = 121836$

Step 2 of 2 :

Find average of square of natural numbers from 1 to 71

Hence the required average

$\displaystyle \sf{ = \frac{121836}{71} }$

$\sf = 1716$

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