On Ursula's birthday, she decides to give away all the money in her bank account to charity.

She gives £100 to the first charity, and then in addition 1/10 of whatever is then left in the account.

Next she gives £200 to the second charity, and in addition 1/10 of whatever is then left in the account.

Next she gives £300 to the third charity, and in addition 1/10 of whatever is then left in the account.

And so on.

When she has given away all her money, she finds that she has given the same amount to every charity.

To how many charities did Ursula make a donation?