The sum of squares of first n natural numbers is n (n+1)(2n+1)/6
Eg the sum of 1
^{2} + 2^{2} + 3^{2} + 4^{2} + ………. +12^{2} =??
= 12 (12+1) (2*12 + 1) /6
= 12*13*25 /6 = 650
The sum of first n even numbers= n (n+1)
Eg The sum of 2+4+6+8+10+…………. +40 = ??
Here n ≠40. N is the no of terms. So number of terms here is 20, the value of 20
^{th} term is 40 indeed. So with n = 20
To find the squares of numbers near numbers of which squares are known
For eg you might know squares of 20,30,40,.. Very easily.
So
To find square of 41 which is near to 40,
Add 40+41 to 1600 =1681
To find 59
^{2} , which is near to 60, Subtract 60^{2 } - (60+59) =3600-119 = 3481
Add when the number is more and subtract when the number is less.
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