Q24 of 79 Page 25

If is the mean of the ten natural numbers, x1, x2, x3,…., x10, show that

(x1-)+(x2-)+ ….+(x10-)= 0.

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


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