Math Is Fun Forum

sandeep8557981588

Guest

about squares of numbers

Firstly I hate math really specially squares of number and algebra . then I suddenly got interest and now  I only do math whole day and math behind magic
I get onto a magic that is :-

1 ( first odd number)                              = 1^2 = 1
1+3 ( sum of first two odd numbers ) = 2^2 = 4
1+3+5   ( "" first three odd""")                = 3^2 = 9
1+3+5+7  ( "" first four odd number"") = 4^2 = 16
And so on

Please help me in finding math behind this magic ppplllleeeeaaaassseeee

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: about squares of numbers

hi sandeep8557981588

Welcome to the forum.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Nemexia

Member

Registered: 2015-05-10

Posts: 13

Re: about squares of numbers

Well there is no magic, its so simple:
as you see

1²-0²=1
2²-1²=3
3²-2²=5
.
.
.
x²-(x-1)²=odd number because:

x²-(x-1)²=x²-(x²-2x+1)=x²-x²+2x-1=2x-1

2k-1 always gives odd numbers