*ALGEBRA :**1.*Sum of first n natural numbers =

*n(n+1)/2*

*2.*Sum of the squares of first n natural numbers =

*n(n+1)(2n+1)/6*

*3.*Sum of the cubes of first n natural numbers =

*[n(n+1)/2]^2*

*4.*Sum of first n natural odd numbers =

*n^2*

*5.*Average =

*(Sum of items)/Number of items*

**An A.P. is of the form a, a+d, a+2d, a+3d, ... where a is called the 'first term' and d is called the 'common difference'**

*Arithmetic Progression (A.P.):**1.*nth term of an A.P.

*tn =*

*a + (n-1)d*

*2.*Sum of the first n terms of an A.P.

*Sn = n/2[2a+(n-1)d]*or

*Sn = n/2(first term + last term)*

**A G.P. is of the form a, ar, ar2, ar3, ... where a is called the 'first term' and r is called the 'common ratio'.**

*Geometrical Progression (G.P.):**1.*nth term of a G.P.

*tn = arn-1*

*2.*Sum of the first n terms in a G.P.

*Sn = a|1-rn|/|1-r|*

**nPr = n!/(n-r)!nPn = n!nP1 = n**

*Permutations and Combinations :*nCr = n!/(r! (n-r)!)nC1 = nnC0 = 1 = nCnnCr = nCn-rnCr = nPr/r!

Number of diagon…