Question

find n if + 3 + 5 + 7 +....
upto n = 225​

Answer 1

Answer:

When we are about to find out the sum of the Series the value of ’n’ has a great role. The answer will be different as we assume ’n’ to be even or odd.

Let us assume that ’n' is even, hence there are equal numbers of positive and negative signed digits.

Therefore 1-3+5-7+9-11... Upto n terms can also be expressed as (1+3+5+7+……upto n terms) -2(3+7+11+…upto n/2

terms) . The 1st part is a A. p having common difference 2 and the first term 1. The 2nd part is a A. P with c. d =4 and first term =3. Hence by calculating it using summation formula we get the the value (-n) when ’n' is even. In case of ’n' being a odd number we can express the sum as (1+3+5+7+9……upto n terms) -2(3+7+11+15+….upto (n-1) /2 terms). As the series always end with a +ve signed digit. Therfore the number of +ve signed digits exceeds the number of -ve signed digits by 1. Again using summation formula we find the value to be equal to +n. Therefore the required sum is +n (when n is a odd number) or (-n) ( when n is even)