If is the mean of the ten natural numbers, x 1 , x 2 , x 3 ,…., x 10 , show that ( x 1 - )+( x 2 - )+ ….+( x 10 - )= 0.

Question

If is the mean of the ten natural numbers, x 1 , x 2 , x 3 ,&#x2026;., x 10 , show that ( x 1 - )+( x 2 - )+ &#x2026;.+( x 10 - )= 0.

Philoid · Accepted Answer

We have, =

x₁ + x₂ + x₃ + …. + x₁₀ = 10 (i)

Now, (x₁ -) + (x₂ -) + …. + (x₁₀ - )

= (x₁ + x₂ + …. + x₁₀) – ( + + …. + up to 1o terms)

= 10 - 10 [From (i)]

= 0

Therefore, (x₁ - ) + (x₂ - ) + …. + (x₁₀ - ) = 0

Hence, proved