@abakcus @mathladyhazel Merci, très beau ! Si on fait une itération de plus, c’est joli à droite: (1234567890 + 10) x 8 + 10 = 9876543210, mais c’est moins beau à gauche... 1234567900 x 8 + 10 = 9876543210 Dommage !!! Toute belle chose à une fin !

@abakcus the "times 8" have to be justified 🤪

@abakcus 12,345,679*(n*9)=nnn,nnn,nnn

@abakcus @DeepakNambisan I love this.

@abakcus It's all because 10 - 2 = 8

@abakcus Let b be the base (in this case 10) n = line number, 1<=k<=n The pattern is n + (b-2)*sum_k k*b^(n-k) = sum_k (b-k)*b^(n-k) Combine both sums n = sum_k (b-k)*b^(n-k) + (2-b)*k*b^(n-k) Simplify n = sum_k (1-k)*b^(n-k+1) + k*b^(n-k) Telescope the sum n = n*b^(n-n) - (1-1)*b^(n-1+1)

@abakcus 123456789

@abakcus @AjitPai

@abakcus 0.9 = 10 - 0.1*91 0.89 = 20 - 0.21*91 0.789 = 30 - 0.321*91 0.6789 = 40 - 0.4321*91 0.56789 = 50 - 0.54321*91 0.456789 = 60 - 0.654321*91 0.3456789 = 70 - 0.7654321*91 0.23456789 = 80 - 0.87654321*91 0.123456789 = 90 - 0.987654321*91

@abakcus Beautiful mathematics 👌👍

@abakcus 🤤🤤

@abakcus @GWOMaths >>> total =0 >>> for i in range(1,10): ... total = total + (i*pow(10,(10-i))) ... z = total/pow(10,(10-i)) ... print(8*z+i) ... 9 98 987 9876 98765 987654 9876543 98765432 987654321

@abakcus 29

@abakcus @SteveStuWill @saljurf

@abakcus have you checked this...