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powers

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Joined: 21 Apr 2010
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powers [#permalink] New post 26 Apr 2010, 02:16
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this is a question i got in my practise.. I will be writing ust the question and not the answer as i dont remember the answer and the options.

Please show how i can solve the question within 2 mins..

2+2+2+ 2^2 +2^3 +2^4+ 2^5 +2^6 +2^7+ 2^8+ 2^9
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Status: Nothing comes easy: neither do I want.
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Concentration: Technology, Entrepreneurship
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Re: powers [#permalink] New post 26 Apr 2010, 02:31
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ITC wrote:
this is a question i got in my practise.. I will be writing ust the question and not the answer as i dont remember the answer and the options.

Please show how i can solve the question within 2 mins..

2+2+2+ 2^2 +2^3 +2^4+ 2^5 +2^6 +2^7+ 2^8+ 2^9


2+2+2+ 2^2 +2^3 +2^4+ 2^5 +2^6 +2^7+ 2^8+ 2^9
= 4+2+ 2^2 +2^3 +2^4+ 2^5 +2^6 +2^7+ 2^8+ 2^9


now2+ 2^2 +2^3 +2^4+ 2^5 +2^6 +2^7+ 2^8+ 2^9 is the sum of GP series with a =2 ,r=2 n = 9

sum of series is =\frac{a(r^n -1)}{(r-1)}= \frac{2* (2^9 -1)}{(2-1)}
= 2^{10} - 2
so required sum is =2^{10} - 2 +4 = 2^{10} +2
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Re: powers [#permalink] New post 26 Apr 2010, 02:51
This can be written as 2+(2^2+2^2+2^3+............+2^9)
2^2+2^2 = 2^3
2^3+2^3 = 2^4
so on ..............2^9+2^9 = 2^10

we will be left with 2+2^10 - answer
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Re: powers   [#permalink] 26 Apr 2010, 02:51
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