Formulas to Remember

Here are some more formulae and equations related to the given formulae:

Arithmetic Progression (AP)

  • The n-th term of an AP whose first term is a and the common difference is d is given by: Tn=a+(n1)d
  • The sum of the first n terms of an AP is given by: Sn=n2[2a+(n1)d]

Geometric Progression (GP)

  • The n-th term of a GP whose first term is a and the common ratio is r is given by: Tn=arn1
  • The sum of the first n terms of a GP is given by: Sn=a(rn1)r1,  for r1

Harmonic Progression (HP)

  • The n-th term of an HP whose first term is a and the common difference is d is given by: Hn=1a+(n1)d
  • The sum of the first n terms of an HP is given by: Sn=n2[H1+Hn]

Sum of squares of first n natural numbers

12+22+32++n2=n(n+1)(2n+1)6

Sum of cubes of first n natural numbers

13+23+33++n3=n2(n+1)24

Binomial Theorem

(a+b)n=k=0n(nk)ankbk

Pascal’s Triangle

(nk)=(n1k)+(n1k1)

Sum of n terms of an arithmetic-geometric series

Sn=a(rn1)r1d(1rn)r1,  for r1

Sum of n terms of an alternating harmonic series

Sn=12[H2nHn],  where Hn=k=1n1k



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