Here is ChatGPTs answer
What would be a simplified formula for a sequence like this:
n*10^0+n*10^1+n*10^2+n*10^3…
The given sequence can be written in sigma notation as:
∑(n*10^k) for k=0 to infinity
where ∑ represents the summation operator and k is the index variable that ranges from 0 to infinity.
Using the formula for the sum of an infinite geometric series, we can simplify the above expression as:
∑(n*10^k) for k=0 to infinity = n/(1-10) * ∑(10^k) for k=0 to infinity
= n/-9 * (1/(1-10))
= n/9
Therefore, the simplified formula for the given sequence is n/9.
npub1ar…akg37
2023-04-11 12:33:50
in reply to nevent1q…24q0
Author Public Key
npub1artur379gp42kd39rlsgx703ytke8fwhydytdf6qlezv8mtlqk6q8akg37Published at
2023-04-11 12:33:50Event JSON
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"content": "Here is ChatGPTs answer\n\nWhat would be a simplified formula for a sequence like this:\n\nn*10^0+n*10^1+n*10^2+n*10^3…\n\nThe given sequence can be written in sigma notation as:\n\n∑(n*10^k) for k=0 to infinity\n\nwhere ∑ represents the summation operator and k is the index variable that ranges from 0 to infinity.\n\nUsing the formula for the sum of an infinite geometric series, we can simplify the above expression as:\n\n∑(n*10^k) for k=0 to infinity = n/(1-10) * ∑(10^k) for k=0 to infinity\n\n= n/-9 * (1/(1-10))\n\n= n/9\n\nTherefore, the simplified formula for the given sequence is n/9.",
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