5+55+555+5555+.555555555=

5+55+555+5555+.555555555=

Let f = 1 + 11 + 111 + 1111 +. + 111111111, then 10F = 10 + 110 + 1110 +. + 111111110 + 1111110;
f-10f=1+11-10+111-110+.+111111111-111111110-1111111110;
-9f=1+1+1+1+1+1+1+1+1-1111111110;
f=123456789;
Therefore, 5 + 55 + 555 + 5555 +. 5555 = 5F = 5 * 123456789 = 617283945
If you don't use the process, it's very simple. 5 + 55 + 555 + 5555 = 5 * (1 + 11 + 111 + 1111 +. + 111111);
1 + 11 + 111 + 1111 +. + 111111111 is the sum of 9 numbers, the number of single digits is the sum of 9 ones, and the number of ten digits is the sum of 8 ones. By analogy, we can easily get 1 + 11 + 111 + 1111 +. + 111111111 = 123456789;
After 5 + 55 + 555 + 5555 +. 5555 = 5 * 123456789 = 617283945

5, 555, 555,; find the general term formula

5*(1-10^n)/(1-10)=5*( 10^n-1)/9

Compare the size of 5555 / 55555 and 555 / 5555

55555／5555＝11111／1111＝10+1／1111
5555／555＝1111／111＝10+1／111
1／111>1/1111
10+1／1111 < 10+1／111
5555/55555>555/5555

24 divided by 4 / 9 means ()

The meaning of 24 divided by 4 / 9 is (4 / 9 of a number is 24, find the number)