Sum of special series till 'n' terms

Important

Sum of the first n terms:

  • Sum of the first n natural numbers is $$\frac{n(n+1)}{2}$$
  • Sum of the squares of the first n natural numbers is $$\frac{n(n+1)(2n+1)}{6}$$
  • The sum of cubes of first 'n' natural numbers = $$(\frac{n(n+1)}{2})^{2}$$
  • The sum of first 'n' odd natural numbers= $$n^{2}$$
  • The sum of first 'n' even natural numbers= n(n+1)
  • In any series, if the sum of first n terms is given by $$S_{n}$$,then the $$n^{th}$$ term $$T_{n}=S_{n}-S_{n-1}$$
Question 1

A football squad has 16 players with jerseys named from 1 to 16. They are divided into four sub squads such that the sum of their jerseys is the same. What is the sum?

Question 2

The sum of n terms of a series is $$n^3 + n^2 + n.$$ Find the 10th term

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Sum of special series till 'n' terms

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