100/(1+10%)^0

Question

100/(1+10%)^0 + 150/(1+10%)^1 + 200/(1+10%)^2

Answer 1

(1+10%) = 1.1   and any natural number to the 0 power is 1.  So the expression becomes

 

100/1 + 150/1.1 + 200/(1.1)²   which is approximately 100 +  136.3636364 + 165.2892562  =  401.6528926

Answer 2

100/(1+10%)^0 + 150/(1+10%)^1 + 200/(1+10%)^2

= 100/1 + 150/1.1 + 200/(1.1*1.1)

= 100 + 1500/11 + 20000/(11*11)

= 100*121/121 + 1500*11/121 + 20000/121

= (12100 + 16500 + 20000)/121

= 48600/121 exactly

Answer 3

First realize that any nonzero number raised to the zeroth power is 1.  This can be seen by example:

 

N^m/N^m = 1 but can also be represented as N^(m-m) = N⁰   Now compute the sum:

Additionally, (1 + 10%) = 1.1 since 10%=0.1

 

Sum= 100/(1.1)^0 + 150/(1.1) + 200/(1.1)^2  = 401.653 (approx)