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The sum \sum_{k=1}^{n}\left ( 1+2+3+4+...+k \right ) is a polynomial in n of degree

Option: 1

2


Option: 2

3


Option: 3

4


Option: 4

5


Answers (1)

best_answer

 

 

Principle of Mathematical Induction -

Mathematical induction is one of the techniques which can be used to prove a variety of mathematical statements which are formulated in terms of n, where n is a positive integer

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\sum_{k=1}^{n}\left ( 1+2+3+4+...+k \right )

\sum_{k=1}^{n}\frac{k^2+k}{2}= \frac{1}{2}\left ( \sum k^2+\sum k \right )

which is a polynomial of degree 2

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Rishi

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