thank you so much Melody for taking the time to answer my questions,

i'd like to start wiith the first one.

the answer that youve given to question no. 1 , thats not the answer thats present in my book. the answer to it is (x-1 )^x - 1 , my doubt in this was that why are we subtracting one here? the (x-1)^x ca efro forula (n)^r.

2.oh Melody i feel bad to have troubled you for this problem , i was just making 2 silly mistakes. but couldnt see them,thank you for the answer and explanation.

3.

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less than 200,000,000 only containing the digits 1 and 2

1 digit 2

2 digit 2*2=2^2

3 digit 2^3

4 digit 2^4

5 digit 2^5

6 digit 2^6

7 digit 2^7

8 digit 2^8

9 digit 2^8 The biggest value digit must be 1

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your third answer is correct btw!

i have no idea what you did here...otherwise i understand everything after that..... could you pls explain this part ? thank you for the answers!