- #1
avistein
- 48
- 1
Find the sum upto n terms:
1.3.5+3.5.7+5.7.9....tn
I solve it this way:
tn=(2n-1)(2n+1)(2n+3)
Now can I take summation on both sides? How?
I mean when I add 2 on both sides the resultant is 0(2-2=0).Similarly the resultant summation will be zero?
And if I take summation I get one term as 3Ʃ.Now in a book I saw that it is 3n. Why? Summation of 3 will be 3 only as 3 is constant.Please explain.
I got this:
Ʃtn=Ʃ(2n-1)(2n+1)(2n+3)
Ʃtn=Ʃ[(4n^2-1)(2n+3)]
Ʃtn=Ʃ[8n^3 + 12n^2 - 2n - 3]
Ʃtn=Ʃ[8n^3] + Ʃ[12n^2] - Ʃ[2n] -Ʃ[3]
Ʃtn=8*Ʃ[n^3] + 12*Ʃ[n^2] - 2*Ʃ[n] - Ʃ[3]
Now do I require to write them as Ʃ[3] or 3Ʃ (putting a constant outside Ʃ).Please explain the whole summation process.I am stuck here.
1.3.5+3.5.7+5.7.9....tn
I solve it this way:
tn=(2n-1)(2n+1)(2n+3)
Now can I take summation on both sides? How?
I mean when I add 2 on both sides the resultant is 0(2-2=0).Similarly the resultant summation will be zero?
And if I take summation I get one term as 3Ʃ.Now in a book I saw that it is 3n. Why? Summation of 3 will be 3 only as 3 is constant.Please explain.
I got this:
Ʃtn=Ʃ(2n-1)(2n+1)(2n+3)
Ʃtn=Ʃ[(4n^2-1)(2n+3)]
Ʃtn=Ʃ[8n^3 + 12n^2 - 2n - 3]
Ʃtn=Ʃ[8n^3] + Ʃ[12n^2] - Ʃ[2n] -Ʃ[3]
Ʃtn=8*Ʃ[n^3] + 12*Ʃ[n^2] - 2*Ʃ[n] - Ʃ[3]
Now do I require to write them as Ʃ[3] or 3Ʃ (putting a constant outside Ʃ).Please explain the whole summation process.I am stuck here.