Question

.Prove a+ar+ar2+………+arn-1=a(rn -1 ) r-1

Answer 1

See below.

Explanation:

Call the sum of the first n terms S.

S = a + ar + ar^2 + ar^3 + ... + ar^(n -1)

Multiply both sides by r.

Sr = ar + ar^2 + ar^3 + ar^4 + ... + ar^n

No subtract S - Sr.

S = a + ar + ar^2 + ar^3 + ar^4 + ... + ar^(n -1)

(-) Sr = ar + ar^2 + ar^3 + ar^4 + ... + ar^(n - 1) + ar^n

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S - Sr = a - ar^n

S(1 - r) = a(1 - r^n)

S = a(1 - r^n)/(1 - r)

S = a(r^n - 1)/(r - 1)

a + ar + ar^2 + ar^3 + ... + ar^(n -1) = a(r^n - 1)/(r - 1)