Advertisements
Advertisements
प्रश्न
Show that `("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!)`
Advertisements
उत्तर
L.H.S. = `("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!)`
= `"n"![1/("r"("r" - 1)!("n" - "r")!) + 1/(("r" - 1)!("n" - "r" + 1)("n" - "r")!)]`
= `("n"!)/(("r" - 1)!("n" - "r")!)[1/"r" + 1/("n" - "r" + 1)]`
= `("n"!)/(("r" - 1)!("n" - "r")!)[("n" - "r" + 1 + "r")/("r"("n" - "r" + 1))]`
= `("n"!)/(("r" - 1)!("n" - "r")!)[("n" + 1)/("r"("n" - "r" + 1))]`
= `(("n" + 1)"n"!)/(["r"("r" - 1)!][("n" - "r" + 1)("n" - "r")!])`
= `(("n" + 1)!)/("r"!("n" - "r" + 1)!)`
= R.H.S.
Hence, `("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!)`
APPEARS IN
संबंधित प्रश्न
Evaluate: 8!
Evaluate: 10! – 6!
Evaluate: (10 – 6)!
Compute: `(12/6)!`
Compute: 3! × 2!
Compute: `(9!)/(3! 6!)`
Compute: `(8!)/(6! - 4!)`
Write in terms of factorial.
5 × 6 × 7 × 8 × 9 × 10
Write in terms of factorial.
3 × 6 × 9 × 12 × 15
Write in terms of factorial.
6 × 7 × 8 × 9
Write in terms of factorial.
5 × 10 × 15 × 20
Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 12, r = 12
Evaluate `("n"!)/("r"!("n" - "r")!)` for n = 15, r = 10
Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 15, r = 8
Find n, if `"n"/(8!) = 3/(6!) + (1!)/(4!)`
Find n, if `"n"/(6!) = 4/(8!) + 3/(6!)`
Find n, if (n + 3)! = 110 × (n + 1)!
Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!
Find n, if: `((15 - "n")!)/((13 - "n")!)` = 12
Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 7)!)` = 1 : 6
Simplify `((2"n" + 2)!)/((2"n")!)`
Simplify `(("n" + 3)!)/(("n"^2 - 4)("n" + 1)!)`
Simplify `("n" + 2)/("n"!) - (3"n" + 1)/(("n" + 1)!)`
Simplify `1/(("n" - 1)!) + (1 - "n")/(("n" + 1)!)`
Simplify `("n"^2 - 9)/(("n" + 3)!) + 6/(("n" + 2)!) - 1/(("n" + 1)!)`
Select the correct answer from the given alternatives.
In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate
Select the correct answer from the given alternatives.
Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.
Eight white chairs and four black chairs are randomly placed in a row. The probability that no two black chairs are placed adjacently equals.
Find the number of integers greater than 7,000 that can be formed using the digits 4, 6, 7, 8, and 9, without repetition: ______
3. 9. 15. 21 ...... upto 50 factors is equal to ______.
Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn + 1 – Tn = 21, then n is equal to ______.
