i read the following ,
(1)^2=1
(11)^2=121
(111)^2=12321
(1111)^2=1234321
how they are making it !
i dont understand the mechanism of this construction..
could you please help me to understand it.
2007-02-06 03:48:21 · 12 answers · asked by sanko 1 in Science & Mathematics ➔ Mathematics
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come on, i understand the multiplication.
i was asking whether its following some pattern or not .
If so, whats the quick way to get the multiplication result without multiplying it.
2007-02-09 18:47:41 · update #1
(1)^2=1*1=1
(11)^2=11*11=121
(111)^2=111*111=12321
(1111)^2=1111*1111=1234321
I think that is the way you figure it out.
2007-02-07 18:09:08 · answer #1 · answered by Dawn 3 · 0⤊ 0⤋
(1)^2= 1 x 1 = 1
(11)^2= 11 x 11 = 121
(111)^2= 111 x 111 = 12321
(1111)^2= 1111 x 1111 = 1234321
2007-02-06 03:52:03 · answer #2 · answered by Sheen 4 · 2⤊ 0⤋
They probably are multiplying 11 * 11, and then 111 * 111, and then 1111 * 1111....
2007-02-06 03:51:40 · answer #3 · answered by bequalming 5 · 0⤊ 0⤋
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2016-11-25 20:16:07 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Interesting pattern... any number composed of n 1s when squared will result in a number 2n-1 digits long, with n in the middle and n-1, n-2,...1 expanding out from left to right.
So... to follow the pattern (up to 9 digits):
11111^2 = 123454321
111111^2 = 12345654321
1111111^2 = 1234567654321
11111111^2 = 123456787654321
111111111^2 = 12345678987654321
Interstingly...
1111111111^2 = 12345678900987654321
2007-02-06 03:58:22 · answer #5 · answered by disposable_hero_too 6 · 0⤊ 1⤋
maybe this will help: 1 = 1^2
121 = 11^2
12321 = 111^2
1234321 = 1111^2
123454321 = 11111^2
and so on.... it forms a pyramid (I think it's called pascal's triangle or pascal's pyramid).
2007-02-06 03:53:28 · answer #6 · answered by Anonymous · 0⤊ 1⤋
1*1=1
11*11=121
111*111=12321
1111*1111=1234321
2007-02-06 03:51:54 · answer #7 · answered by Male_42_us 2 · 2⤊ 0⤋
Check out this:
12345679 x 9 =
12345679 x 18 =
12345679 x 27 =
12345679 x 36 =
12345679 x 45 =
12345679 x 54 =
12345679 x 63 =
12345679 x 72 =
12345679 x 81 =
2007-02-06 03:55:27 · answer #8 · answered by Mikhil M 2 · 1⤊ 1⤋
It's saying 1x1 is 1, 11x11 is 121...
(b)^a=x
What this means is b must be all ones for this to apply, but for however many digits b is, x will be the palendrome starting from one going to that number. For example, b is 11111, that's five digits, so x goes to five both ways, 123454321.
2007-02-06 03:53:10 · answer #9 · answered by geobrad7 2 · 1⤊ 1⤋
This all comes from plugging x=10 into these equalities:
(1 + x)² = 1 + 2x + x²
(1+x+x²)² = 1 + 2x + 3x² + 2x³ + x^4
etc.
2007-02-06 03:59:43 · answer #10 · answered by Anonymous · 0⤊ 1⤋