Recent questions tagged principle of mathematical induction

+1 vote

1 answer

State whether the following proof (by mathematical induction) is true or false for the statement.

asked Apr 7, 2019 in Mathematics by kratos

+2 votes

1 answer

1/(1.4) + 1/(4.7) + 1/(7.10) + ......+ 1/(3n - 2)(3n + 1)) = n/(3n + 1)

asked Apr 7, 2019 in Mathematics by kratos

+2 votes

1 answer

The Boolean expression ((p ∧ q) ∨ (p ∨ ~q)) ∨ (~ p ∧ ~q) is equivalent to :

asked Apr 4, 2019 in Mathematics by kratos

+3 votes

1 answer

1/1.2 + 1/2.3 + 1/3.4 + .... + 1/n(n + 1) = n/(n + 1) for all n ∈ N

asked Mar 31, 2019 in Mathematics by kratos

+3 votes

1 answer

If f(x) = Π (x - n)^n(101 - n) for n ∈ [1, 100], where Πai for i ∈ [1, k] stands for product a1 .a2 .......... ak , then f(101)/f'(101) =

asked Mar 30, 2019 in Mathematics by kratos

+1 vote

1 answer

If p(n) : n^2 > 100 then (A) p(1) is true (B) p(4) is true (C) p(k) is true k ≥ 5, k ∈ N

asked Mar 30, 2019 in Mathematics by kratos

+1 vote

1 answer

By Principle of Mathematical Induction, prove that for all n ∈ N a + ar + ar^2 + ..... n terms = {a(r^n-1)}/(r-1), if r ≠ 1

asked Mar 25, 2019 in Mathematics by kratos

+1 vote

1 answer

∀ n ∈ N, P(n): 2.7^n + 3.5^n - 5 is divisible by .....

asked Mar 22, 2019 in Mathematics by kratos

+2 votes

1 answer

(2n + 7) < (n + 3)^2

asked Mar 21, 2019 in Mathematics by kratos

+1 vote

1 answer

For all positive integral values of n, 3^3n - 2n + 1 is divisible by....

asked Mar 18, 2019 in Mathematics by kratos

+3 votes

1 answer

1 + 3 + 3^2 + .... + 3^n - 1 = (3^n - 1)/2

asked Mar 12, 2019 in Mathematics by kratos

+1 vote

1 answer

For each n ∈ N, 10^2n-1 + 1 is divisible by .....

asked Mar 12, 2019 in Mathematics by kratos

+3 votes

1 answer

3^2n+2 - 8n - 9 is divisible by 8.

asked Mar 10, 2019 in Mathematics by kratos

+1 vote

1 answer

For n ∈ N, 3^2n + 2 – 2^3 n – 9 is divisible by (a) 3 (b) 9 (c) 64

asked Mar 10, 2019 in Mathematics by kratos

+2 votes

1 answer

A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mas M and radius R attached rigidly

asked Mar 8, 2019 in Mathematics by kratos

+3 votes

1 answer

For all n ∈ N, a^n - b^n is always divisible by.....(a and b are distinct rational numbers)

asked Mar 6, 2019 in Mathematics by kratos

+1 vote

1 answer

lim(n →∞) (1 + √2 + √3 + ......+√n)/n^3/2 is equal to

asked Mar 4, 2019 in Mathematics by kratos

+3 votes

1 answer

If p → (~p∨ ~ q) is false, then the truth values of p and q are, respectively,

asked Mar 4, 2019 in Mathematics by kratos

+1 vote

1 answer

By Principle of Mathematical Induction, prove that for all n ∈ N. Show that x^n – y^n is divisible by x – y for all n ∈ N.

asked Feb 28, 2019 in Mathematics by kratos

+3 votes

1 answer

For each n ∈ N, the correct statement is .....

asked Feb 25, 2019 in Mathematics by kratos

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