Home
Class 12
MATHS
Find the sum of sum(r=1)^n r* (nCr)/(nC(...

Find the sum of `sum_(r=1)^n r* (nC_r)/(nC_(r-1)`

Text Solution

Verified by Experts

`underset(r=1)overset(n)sum(r.^(n)C_(r))/(.^(n)C_(r-1))=underset(r=1)overset(n)sumr(n-r+1)/(r)`
`= (n+1)underset(r=1)overset(n)sum1-underset(r=1)overset(n)sumr`
`=n(n+1)-(n(n+1))/(2)`
`= (n(n+1))/(2)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Example|10 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 8.1|17 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

Similar Questions

Explore conceptually related problems

Find the sum sum_(r=1)^n r^n (^nC_r)/(^nC_(r-1)) .

If sum_(r=1)^n T_r=(3^n-1), then find the sum of sum_(r=1)^n1/(T_r) .

Find the sum sum_(r=1)^n r(r+1)(r+2)(r+3)

Find the sum sum_(r=1)^(n) r^(2) (""^(n)C_(r))/(""^(n)C_(r-1)) .

Find the sum of the series sum_(r=1)^n r/((r+1) !)dot

Find the sum sum_(r=0) .^(n+r)C_r .

The value of sum_(r=1)^n (^nP_r)/(r!) is

Find the value of sum_(r=1)^(n) (r)/(1+r^(2)+r^(4))

Find the sum sum_(r=0)^(5)""^(32)C_(6r) .

Find the sum sum_(r=1)^n r/((r+1)!) where n!= 1xx2xx3....n .