Few Interesting Series of 33333.....

3 x 37 = 111

33 x 3367 = 111,111

333 x 333667 = 111,111,111

3333 x 33336667 = 111,111,111,111

33333 x 3333366667 = 111,111,111,111,111

33^2 = 65^2 - 56^2

3333^2 = 6565^2 - 5656^2

333333^2 = 656565^2 - 565656^2

33333333^2 = 65656565^2 - 56565656^2

3333333333^2 = 6565656565^2 - 5656565656^2

165033 = 16^3 + 50^3 + 33^3 and

1000165033 = 1000^3 + 16^3 + 50^3 + 33^3

Another Interesting Series

8 x 8 + 13 = 77
88 x 8 + 13 = 717
888 x 8 + 13 = 7117
8888 x 8 + 13 = 71117
88888 x 8 + 13 = 711117
888888 x 8 + 13 = 7111117
8888888 x 8 + 13 = 71111117
......................... and so on



Note:
(88888......)*8  + 13 = 711....1117

If numbers of 8s in bracket of LHS is "n" then number of 1s in RHS is (n-1)

You might get a question in your examination

(888........is a 101 digits number)*8 + 13 = N
then, what would be sum of digits of N?

Ans: 114

Sol: Since there are 101 8s in LHS so there should in 100 1s in RHS sandwiched between two 7s.

So, total digit sum = 7 + 100*1 + 7 = 114