Let Sn denote the sum of the cubes of fi...

Let `S_n` denote the sum of the cubes of first `n` nastural numbers and `s_n` denote the sum of first `n` natural numbers. Then, write the value of `sum_(r=1)^n(S_r)/(s_r)dot`

`(n(n+1)(n+2))/6`

`(n(n+1))/2`

`(n^2 + 3n+2)/6`

`(n^2 + 3n+ 2) /3`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise LEVEL-2|34 Videos
SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos
SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos
REVISION TEST-2 JEE
VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos
STRAIGHT LINES
VMC MODULES ENGLISH|Exercise JEE Advanced Archive (State true or false: Q. 42)|1 Videos

Similar Questions

Explore conceptually related problems

Write the sum of first n odd natural numbers.

let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of the first n natural numbers , then sum_(r=1)^(n)(S_(r))/(s_(r)) equals to

Write the sum of first n even natural numbers.

Let S_n denote the sum of the cubes of the first n natural numbers and s_n denote the sum of the first n natural numbers. Then sum_(r=1)^n S_r/s_r is equal to

Let S_(n) denote the sum of the cubes of the first n natural numbers and s_(n) denote the sum of first n natural numbers then (S_(n))/(s_(n)) is equal to (i) (n(n+1)(n+2))/6 (ii) (n( n+1))/2 (iii) (n^(2)+3n+2)/2 (iv) (2n+1)/3

If S_(n) denotes the sum of the products of the products of the first n natureal number taken two at a time

For some natural number 'n', the sum of the first 'n' natural numbers is 240 less than the sum of the first (n+5) natural numbers. Then n itself is the sum of how many natural numbers starting with 1.

If S_n denotes the sum of first n natural number then S_1 + S_2x + S_3 x^2 +……+S_n x^(n-1) + ……oo terms =

Let S_n denotes the sum of the first of n terms of A.P. and S_(2n)=3S_n . then the ratio S_(3n):S_n is equal to

VMC MODULES ENGLISH-SEQUENCE AND SERIES -LEVEL-1

Value of 1+1/(1+2)+1/(1+2+3)+....+1/(1+2+3+....+n) is equal to
Text Solution
|
If sum(r=1)^n I(r)=(3^n -1) , then sum(r=1)^n 1/(I(r)) is equal to :
Text Solution
|
Let Sn denote the sum of the cubes of first n nastural numbers and sn ...
Text Solution
|
If Sn=sum(r=1)^n(1+2+2^2+ .......+2^r)/(2^r), then Sn is equal to (a)2...
Text Solution
|
If a > 1, b > 1, then the minimum value of logb a + loga b is
Text Solution
|
Let tn =n.(n!) Then sum(n=1)^(15) tn is equal to
Text Solution
|
A series whose n^(th) term is (n/x), then sum of r terms will be
Text Solution
|
x gt0, then the sum of the series e^(-x)-e^(-2x)+e^(-3x)-... i s
Text Solution
|
Find the sum up to 20 terms. 1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+
Text Solution
|
Find the 1+2.2+3.2^2+…….+tn
Text Solution
|
The sum of the first n terms of the series 1^2+2xx2^2+3^2+2xx 4^2+5^2+...
Text Solution
|
sum(r=1)^n r (n-r +1) is equal to :
Text Solution
|
The arithmetic mean between two numbers is A and the geometric mean is...
Text Solution
|
If S(n)=1+(1)/(2)+(1)/(2^(2))+"..."+(1)/(2^(n-1)), then calculate the ...
Text Solution
|
If a, b, c are positive real numbers, then the minimum value of a^(l...
Text Solution
|
If an>1 for all n in N then log(a2) a1+log(a3) a2+.....log(a1)an has t...
Text Solution
|
The least value of 2log100 a-loga 0.0001 , a >1
Text Solution
|
If in a series tn=n/((n+1)!) then sum(n=1)^20 tn is equal to :
Text Solution
|
Let f(n) = [1/2 + n/100] where [x] denote the integral part of x. Then...
Text Solution
|
The value of sum(r=1)^n1/(sqrt(a+r x)+sqrt(a+(r-1)x)) is -
Text Solution
|