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What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)

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Re: What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)

by regor60 » Mon Nov 29, 2021 7:06 am
Let expression = S.

S/5 = 1+4+4*5+4*5^2+4*5^3+4*5^4
which equals

S-4*5^5

So, S/5 = S- 4*5^5.

S-S/5= 4*5^5

4/5S = 4*5^5

S= (5/4)*4*5^5= 5*5^5=[spoiler]5^6,A[/spoiler]
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Re: What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)

by Ian Stewart » Wed Dec 01, 2021 5:00 am
Gmat_mission wrote: ↑
Sun Nov 28, 2021 6:51 am
 What is the value of \(5+4\cdot 5+4\cdot 5^2+4\cdot 5^3+4\cdot 5^4+4\cdot 5^5?\)
You can also replace "4" with "5 - 1", so the expression becomes

5 + (5-1)*5 + (5-1)*5^2 + (5-1)*5^3 + (5-1)*5^4 + (5-1)*5^5
= 5 - 5 + 5^2 - 5^2 + 5^3 - 5^3 + 5^4 - 5^4 + 5^5 - 5^5 + 5^6
= 5^6
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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