npub1ar…akg37 on Nostr: Here is ChatGPTs answer What would be a simplified formula for a sequence like this: ...
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.
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.