Advertisements
Advertisements
Question
If S1, S2, S3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that `9S_2^2 = S_3(1 + 8S_1)`
Solution
From the given information,
APPEARS IN
RELATED QUESTIONS
Write the first five terms of the sequences whose nth term is:
`a_n = n(n+2)`
Write the first five terms of the sequences whose nth term is:
`a_n = n/(n + 1)`
Write the first five terms of the sequences whose nth term is:
an = 2n
Write the first five terms of the sequences whose nth term is:
`a_n = (2n -3)/6`
Write the first five terms of the sequences whose nth term is:
`a_n = (-1)^(n-1) 5^(n+1)`
Write the first five terms of the sequences whose nth term is:
`a_n = n (n^2 + 5)/4`
Find the indicated term in the following sequence whose nth term is:
an = 4n – 3; a17, a24
Find the indicated term in the following sequence whose nth term is:
`a_n = n^2/2^n`; `a_7`
Find the indicated term in the following sequence whose nth term is:
`a_n = (–1)^(n – 1) n^3; a_9`
Find the indicated term in the following sequence whose nth term is:
`a_n = (n(n-2))/(n+3)` ;`a_20`
The Fibonacci sequence is defined by 1 = a1 = a2 and an = an – 1 + an – 2, n > 2.
Find `a_(n+1)/a_n`, for n = 1, 2, 3, 4, 5
If θ1, θ2, θ3, ..., θn are in A.P., whose common difference is d, show that secθ1 secθ2 + secθ2 secθ3 + ... + secθn–1 . secθn = `(tan theta_n - tan theta_1)/sin d`
Two sequences cannot be in both A.P. and G.P. together.
Every progression is a sequence but the converse, i.e., every sequence is also a progression need not necessarily be true.
| Column I | Column II |
| (a) `4, 1, 1/4, 1/16` | (i) A.P |
| (b) 2, 3, 5, 7 | (ii) Sequence |
| (c) 13, 8, 3, –2, –7 | (iii) G.P. |
