Numbers

929865843

3-units(10^0)
4-tens(10^1)
8-hunders(10^2)
5-thousands(10^3)
6-ten thousands(10^4)
8-lacs(10^5)
9-ten lacs(10^6)
2-crores(10^7)
9-ten crores(10^8)

Place value or local value.

is the number which is obtained by multiplication of that number with place value. for 7890
The local value of 9 is 9 *10 = 90

Face value

Face value of any number is that number itself.
face value of 9 is 9 itself.

commutative law

a * ( b + c) = (a * b) + (a * c)
a * ( b - c) = (a * b) - (a * c)

Squares and cubes

(a+b)^2 = a * a + 2 * a * b + b * b
(a+b)^3 = a * a * a + 3 * a * a * b + 3 * a * b * b + b * b * b
(a+b+c)^2 = a * a + b * b+ c * c+ 2 *( a * b + b * a + b * c)
(a+b) (a-b) = a*a - b*b

Summation series

1 + 2 + 3 + ..... + n = n * (n+1) / 2

1 + 4 + 9 + 16 + .... + n * n =
n * (n + 1 ) * (n + 2) / 6

1 + 8 + 27 + 64 + 125 ... + n * n * n =
n * n * (n+1) * (n+1) / 4

In Arithmetic progression(A.P)

Tn = a + (n-1) * d.
Where
Tn= nth term
a = first term
d = difference between two terms
n = number of terms
The sum of n terms in A.P
sn= n * [ 2 * a + ( n - 1 ) * d) / 2
= n [first term + last term] / 2

Geomentric progression

if terms are a*r, a*r*r, a*r*r*r,...
then
Tn= a * r^(n-1)

Sum of the terms
Sn = a * ( 1 - r^n) / (1 - r)
a = first term
r = common ratio.