prove that the sum of n terms of am between a & b is n times the am between a & b
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Let A 1, A 2 ........ An be n A.M. between two numbers a and b
Then a, A 1, A 2 ..... An , b is in A.P. with
Common difference (d) = (b-a)/(n+1)
So,
A1+ A2+ .........An= n/2(A1+An)
= n/2(A1-d+An+d)
= n/2(a+b)
= n* (a+b)/2
Then a, A 1, A 2 ..... An , b is in A.P. with
Common difference (d) = (b-a)/(n+1)
So,
A1+ A2+ .........An= n/2(A1+An)
= n/2(A1-d+An+d)
= n/2(a+b)
= n* (a+b)/2
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