Show that the ratio of the sum of first n terms of a G.P to the sum of terms from (n+1)th to (2n)th term is 1/(r)n(1divided by r to the power n)..? please answer it as fast as possible...
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,349 answers
starTop subjects are Math, Science, and Business
You need to remember how to evaluate the sum of n terms of geometric progression such that:
`S_n_1 = (a_1)*(r^n - 1)/(r-1)`
Notice that 1 represents the value of the first terms of geometric progression and r represents the common ratio.
You need to evaluate the sum of the n terms of the same geometric progression, having the first term `n+1` and the same common ratio r such that:
`S_n_2 = (a_(n+1))*(r^n - 1)/(r-1)`
You need to evaluate the following ratio such that:
`(S_n_1)/(S_n_2) = ((a_1)*(r^n - 1)/(r-1))/(a_(n+1)*(r^n - 1)/(r-1))`
Reducing like terms yields:
`(S_n_1)/(S_n_2) = (a_1)/(a_(n+1))`
You need to remember that you may write the `a_(n+1)` term using the first term and the common ratio such that:
`(a_(n+1)) = a_1*r^n`
`(S_n_1)/(S_n_2) = (a_1)/(a_1*r^n)`
Reducing like terms yields:
`(S_n_1)/(S_n_2) = 1/r^n`
Hence, evaluating the ratio `(S_n_1)/(S_n_2)` yields `(S_n_1)/(S_n_2) = 1/r^n` .
Related Questions
- The first term of a G.P. is 1. The sum of the third and fifth term is 90. Calculate the common...
- 1 Educator Answer
- The sum of the first three terms of G.P. is 7 and sum of their squares is 21. Calculate first...
- 1 Educator Answer
- Prove the relation: 1² + 2² + 3² ... n² = 1/6 n(n+1)(2n+1)
- 1 Educator Answer
- Prove that n C r + n C r-1 = n+1 C r
- 1 Educator Answer
- the coifficent of {r-1}th ,r th ,{r-1}th term in expansion of {x+1}n are in the ratio 1:3:5,find...
- 1 Educator Answer
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.