Home
Class 11
MATHS
The sum of the series Sigma(r = 0)^(10) ...

The sum of the series `Sigma_(r = 0)^(10) ""^(20)C_(r) " is " 2^(19) + (""^(20)C_(10))/(2)`

Text Solution

Verified by Experts

Given series `= underset(r = 0)overset(10)Sigma .^(20)C_(r) = .^(20)C_(0) + .^(20)C_(1) + .^(20)C_(2) + ... + .^(20)C_(10)`
`= .^(20)C_(0) + .^(20)C_(1) +..... + .^(20)C_(10) + .^(20)C_(11) + ... .^(20)C_(20) - (.^(20)C_(11) + .... + .^(20)C_(20))`
`= 20^(20) - (.^(20)C_(11) + ... + .^(20)C_(20))`
Hence, the given statement is false
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    NCERT EXEMPLAR|Exercise Objective type question|16 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos

Similar Questions

Explore conceptually related problems

The sum of the series sum_(r=0) ^(n) "r."^(2n)C_(r), is

The sum of the series sum_(r=0) ^(n) ""^(2n)C_(r), is

Sum of the series Sigma_(r=1)^(n) rlog((r+1)/(r)) is

sum_(r=0)^(20).^(50-r)C_6

The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

Find the sum of the series sum_(r=0)^(50)(""^(100-r)C_(25))/(100-r)