Question

examine the nature of series 1+2+3+4+...n+...infinitive ​

Answer 1

Answer:

5+6+7+8+9+10+ infinite

Answer 2

Answer:

Arithmetic Progression

Step-by-step explanation:

Given that a series 1 + 2 + 3 + 4 + 5 + ...+ n

To find the nature of the series .

So,

In this series ,

common difference ( d ) = a2 - a1

                                        = 2 - 1

                                        = 1

Therefore , this series is in Arithmetic Progression ( A.P. )

By using the formula of A.P. for sum.

  Sn = $\frac{n}{2}(2a+(n-1)d$

where a = 1 and d = 1.

  Sn =$\frac{n}{2}(2*1+(n-1)*1)$

  Sn = $\frac{n}{2}( 2+n-1)$

  Sn = $\frac{n}{2}(n+1)$

Therefore sum of natural number from 1 to infinite is $\frac{n}{2}(n+1)$.

THANKS.

#SPJ3.

https://brainly.in/question/19686824