Home
Class 12
MATHS
If sum(i=1)^(10) ( (""^10C(i-1))/(""^10...

If ` sum_(i=1)^(10) ( (""^10C_(i-1))/(""^10C_i + ""^10C_(i-1) ))^3 = (k)/(11)` , then k equals :

Text Solution

Verified by Experts

`(""^10C_(i-1) )/(""^10C_i + ""^10C_(i-1) ) = (""^10C_(i-1) )/(""^11C_i)`
`( (10!)/((10 - I + 1 ) !(i-1)!))/((11!)/((11 - i)!i!)) = (10!)/((10 - i+ 1) (i-1)!) xx ((11-i)!i!)/(11!)`
` sum_(i=1)^(10) (i^3)/(11^3) = (k)/(11) , (10^2 xx 11^2)/(4 xx 10^3) =(k)/(11)`
k = 25
Promotional Banner

Similar Questions

Explore conceptually related problems

If Sigma_(i=1)^(20) ((""^(20)C_(i-1))/(""^(20)C_(i)+""^(20)C_(i-1)))^(3)=(k)/(21) , then k equals

If sum_(i=1)^(20)((""^(20)C_(i-1))/(""^(20)C_(i)+""^(20)C_(i=1)))^(3)=k/21 , then k/20 equals _________.

If sum_(i=1)^(n-1) ((""^(n)C_(i-1))/(""^(n)C_(i)+""^(n)C_(i-1)))^(3) = (36)/(13) , , then n is equal to

sum_(i=1)^20 (.^20C_(i-1))/(.^20C_i+.^20C_(i-1))=k/21 then find the value of k. (a) 400 (b) 100 (c) 50 (d) 200

If sum_(r=1)^(10).^(10)C_(r)(2)^(20-r)(3)^(r-1)=(a^(10)-b^(10))/(3) then (a-b) is equal to

The value of sum_(r=0)^(9)(10C_(r))/(^^^10C_(r)+^(10)C_(r+1)) is equal to

sum_ (k = 1) ^ (10) ((sin (2k pi)) / (11) + i (cos (2k pi)) / (11))