Advertisements
Advertisements
Question
Choose the correct alternative:
1 + 3 + 5 + 7 + · · · + 17 is equal to
Options
101
81
71
61
Solution
81
APPEARS IN
RELATED QUESTIONS
By the principle of mathematical induction, prove the following:
4 + 8 + 12 + ……. + 4n = 2n(n + 1), 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.
By the principle of mathematical induction, prove the following:
n(n + 1) (n + 2) is divisible by 6, for all n ∈ N.
The term containing x3 in the expansion of (x – 2y)7 is:
By the principle of mathematical induction, prove that, for n ≥ 1
12 + 32 + 52 + ... + (2n − 1)2 = `("n"(2"n" - 1)(2"n" + 1))/3`
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 ≥ 2,
`1/(1 + 2) + 1/(1 + 2 + 3) + 1/(1 +2 + 3 + 4) + .... + 1/(1 + 2 + 3 + ... + "n") = ("n" - 1)/("n" + 1)`
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
Using the Mathematical induction, show that for any natural number n, x2n − y2n is divisible by x + y
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 10n + 3 × 4n+2 + 5, is divisible by 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:
In 3 fingers, the number of ways four rings can be worn is · · · · · · · · · ways
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 ______
