Question

3+7+11+15+19+23+27......
Express t1 in terms of s1

Answer 1

Solution:

S=3+7+11+15+19+23+27......    --------------(1)

This is an Arithmetic series having , 3 as first term and Common difference=7-3=4.

Why Arithmetic series as difference between two consecutive terms is same in each case.

S=    3+7+11+15+19+23+27......     -----------------(2)

Equation (1) - Equation (2)

0=3 +4+4+4.......upto infinity

0= sum of natural number up to infinity

0=∞, which is not possible.

Hence , as common difference of this Arithmetic progression is 4, which is positive.

So, $S_{I}=3+7+11+15+19+23+27......=I$

Where , I= Infinity