Adding Powers

[pseizert]

Had this question in a practice exam. Seemed too easy when I took it; turns out my feelings were correct and I got the answer wrong. Any insights?

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =

a:2^9
b:2^10
c:2^16
d:2^35
e:2^37

[stud.jatt]

the key in solving this quickly lies in realizing that

2^x + 2^x = 2*2^x = 2^(x+1)

start with the first two terms

2 + 2 = 2^2

then add the next one to this

2^2 + 2^2 = 2^3

repeating the same step

2^3 +2^3 = 2^4 and so one...

you don't have to calculate all the way to 2^8, just a cursory look at this pattern will tell you that the last two terms we will have are

2^8 + 2^8 = 2^9 which is the answer

Had this question in a practice exam. Seemed too easy when I took it; turns out my feelings were correct and I got the answer wrong. Any insights?

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =

a:2^9
b:2^10
c:2^16
d:2^35
e:2^37

[RonPurewal]

read here:
post25467.html#p25467

this thread is now locked. PLEASE search the forum for existing threads before you post -- we don't want to create a million zillion threads about the same problem. thanks.