Series question

[imnerd]

Hi, all. I have a question about series.

Given that the sum of the first n terms of a series is [n log(pq)^(n+1)].
Show that

i)the nth term of series is log(pq)^2n,
ii)this is an arithmetic series

how to find the sum of first n terms of series if we dont know the exact value? Plz help me, thank you

 

[tkhunny]

1) log(p*q) seems to be an unnecessary complication. Get rid of it and just call it r. This gives the sum of the first n terms as S_n = n*rⁿ⁺¹, quite a bit simpler looking.

2) If each sequential term is identified as a_i, then it should be intuitive that a_n = S_n - S_n-1 and you can find an expression for a_n.

 

[imnerd]

To determine the sequential term in a series, we use an = Sn - Sn-1.

Sn is n*(r)^n+1 but how about Sn-1?

help out plz

 

[jimi]

S(n-1) = (n-1)r^((n-1)+1) = (n-1)r^n
just replace n with n-1.

the nth term is then Sn - S(n-1), as tkhunny has stated, i.e.
nr^(n+1) - (n-1)r^n
Since log(a)^b = b log a for any a and b, r^n = nr and r^(n+1) = (n+1)r
I'll leave you to finish it.

 

[imnerd]

:idea: i get the point, thx!