perplexus.info :: Numbers : Quick p&p problem

Quick p&p problem (Posted on 2024-10-07)

Using only p&p(no calculator), determine the value of:

9⁵+9⁴+9³+9²+9

No Solution Yet Submitted by K Sengupta

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Possible Solution

| Comment 2 of 3 |

Note that x^n-1= (x-1)(x^(n-1)+x^(n-2)...+x+1)

Substitute and divide back by (x-1):

(9^6-1)/(9-1)= ((9^2)^3-1)/(8)

Working:

81^3=6561*81=531441

531441-1=531440

531440/8=66430

Take away the 1 we added = 66429

Posted by broll on 2024-10-12 02:14:50

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