Advertisements
Advertisements
प्रश्न
The term containing x3 in the expansion of (x – 2y)7 is:
विकल्प
3rd
4th
5th
6th
Advertisements
उत्तर
5th
APPEARS IN
संबंधित प्रश्न
By the principle of mathematical induction, prove the following:
1.2 + 2.3 + 3.4 + … + n(n + 1) = `(n(n + 1)(n + 2))/3` for all n ∈ N.
By the principle of mathematical induction, prove the following:
32n – 1 is divisible by 8, for all n ∈ N.
By the principle of mathematical induction, prove the following:
52n – 1 is divisible by 24, for all n ∈ N.
Prove that the sum of the first n non-zero even numbers is n2 + n
Using the Mathematical induction, show that for any natural number n,
`1/(1*2*3) + 1/(2*3*4) + 1/(3*4*5) + ... + 1/("n"("n" + 1)*("n" + 2)) = ("n"("n" + 3))/(4("n" + 1)("n" + 2))`
Prove by Mathematical Induction that
1! + (2 × 2!) + (3 × 3!) + ... + (n × n!) = (n + 1)! − 1
By the principle of Mathematical induction, prove that, for n ≥ 1
`1^2 + 2^2 + 3^2 + ... + "n"^2 > "n"^2/3`
Use induction to prove that 5n+1 + 4 × 6n when divided by 20 leaves a remainder 9, for all natural numbers n
Prove that using the Mathematical induction
`sin(alpha) + sin (alpha + pi/6) + sin(alpha + (2pi)/6) + ... + sin(alpha + (("n" - 1)pi)/6) = (sin(alpha + (("n" - 1)pi)/12) xx sin(("n"pi)/12))/(sin (pi/12)`
Choose the correct alternative:
Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is ______
