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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solution

| Comment 1 of 3

In analogy with 10^5+10^4+10^3+10^2+10

= ((10^5-1)/9)*10:

9^5+9^4+9^3+9^2+9

= ((9^5-1)/8)*9

as it represents a repunit times the base in base-9 rather than base ten.

Posted by Charlie on 2024-10-07 09:38:05

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