exponents

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gmataug08: Master | Next Rank: 500 Posts; Posts: 105; Joined: Sat May 17, 2008 8:12 pm; Thanked: 6 times

exponents

by gmataug08 » Wed Nov 26, 2008 10:52 am

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

Is there any formula or tricks to approach this problem?

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Source: Beat The GMAT — Problem Solving | Wed Nov 26, 2008 10:52 am

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pm; Location: Pittsburgh, PA; Thanked: 113 times; Followed by:27 members; GMAT Score:710

by dmateer25 » Wed Nov 26, 2008 11:10 am

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

2(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7)

2^2(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6)

2^3(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5)

2^4(2 + 2 + 2^2 + 2^3 + 2^4)

2^5(2 + 2 + 2^2 + 2^3)

2^6(2 + 2 + 2^2 )

2^7(2^2)

2^9

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resepulv: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun Aug 03, 2008 4:26 pm

by resepulv » Wed Nov 26, 2008 12:38 pm

Is equal to: 1+SUM(2^i), i=0,...,8
the formula to solve this is: SUM(a^i), i=0,...,n is equal to: (1-a^(n+1))/(1-a).

So the solution is: 1+(1-2^9)/(1-2)=1+2^9-1=2^9