The numbers can take the form\(1a1, 2a2, 3a3.....9a9\) where\(a\) can be\(0-9\)
If we start with 101, since\(a\) is the tens digit, with every value of\(a\) , a value of 101 + 10a is added to the sum
For example, when\(a\) takes three values 0, 1 and 2, their sum is\(101 + 111 + 121 = 101 + (101 + 10*1)+(101 + 10*2)\) or this can be written as\(101*3 + 10 (1+2)\)
Therefore when\(a\) takes\(n\) values, the sum of all numbers of the form\(1a1\) will be \([101*n]+[10*(1+2+..+n-1)]\)
Following the same, when\(a\) takes 10 values (0-9),
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If we start with 101, since\(a\) is the tens digit, with every value of\(a\) , a value of 101 + 10a is added to the sum
For example, when\(a\) takes three values 0, 1 and 2, their sum is\(101 + 111 + 121 = 101 + (101 + 10*1)+(101 + 10*2)\) or this can be written as\(101*3 + 10 (1+2)\)
Therefore when\(a\) takes\(n\) values, the sum of all numbers of the form\(1a1\) will be \([101*n]+[10*(1+2+..+n-1)]\)
Following the same, when\(a\) takes 10 values (0-9),
...
