Question

Prove the riemann sum to the nth term with i=1 of ar^i-1 is equivalent to a(r^n -1)/(r-1).

Answer 1

It remains true as a sum of a finite series with r not equal to 1 according to the formula.

Answer 2

so for i=1 you get

ar^(1-1) = ar^0 = a

and on the other part for n=1

a((r^1 -1)/(r-1)) = a((r-1)/(r-1)) = a*1 = a

sorry here a(r^(n-1))/(r-1) will be right or

a((r^n -1)/(r-1)) or this is right ?

suppose is true for i=k and n=k

than prove for k=k+1 for i and n so than will get

ar^(k+1) = ar^k *r

and on the other part

a((r^(k+1) -1)/(r-1)) = a(r^k *r -1)/(r-1)) =