Prove that the sum of `n` arithmetic means between two numbers in `n` times the single A.M. between them.

Explanation

Let `A_1,A_2,A_3,..,A_n`

Am between a,b

`AP->a,A_1,A_2,...,A_n,b`

`b=a+(n+2-1)d`

`d=(b-a)/(n+1)-(A)`

Now,

`A_1+A_2+...+A_n=n/2[A_1+A_n]`

`a+b=A_1+A_n`

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