TS EAPCET (Engineering) Mathematical Induction — practice questions
73 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) Mathematical Induction in the app →In a proof by induction, which part is established first?What is the assumption made in the induction step called?Which everyday metaphor is used to explain mathematical induction?If P(1) is true and P(k) implies P(k + 1), P(n) holds for what?Does mathematical induction give a probable conclusion or a proof?To prove a statement for all n that are at least 5, which base case is used?Who gave the first explicit formulation of the induction principle in 1665?Around 1000 AD, who wrote the earliest implicit proof by induction?The sum of the first n odd integers, shown by induction, equals what?A staircase has 20 numbered steps. What is 1 + 2 + 3 + ... + 20?Which method, used by Fermat, is a variation of induction?In strong induction, the step assumes the claim for which cases?How do weak and strong induction compare in what they can prove?Strong induction proves every integer above 1 is a product of what?Which amount cannot be made from 4- and 5-dollar coins?The all-horses-one-color induction argument fails in which part?Who proposed the false argument that all horses share one color?Cauchy extended the AM-GM inequality from powers of 2 to all n by what?Induction extended to trees and similar structures is called what?In which century did the modern formal treatment of induction arrive?Which Swiss mathematician employed the induction hypothesis early on?To prove 1 + 3 + ... + (2k - 1) = k squared, which term moves P(k) to P(k + 1)?For 1 + 2 + ... + n = n(n + 1)/2, what is the right side of P(k + 1)?Using the formula n(n + 1)(2n + 1)/6, find 1 squared + ... + 10 squared.The sum of cubes 1 to n equals [n(n + 1)/2] squared. What is 1 cubed to 6 cubed?If 2 + 4 + ... + 2n = n(n + 1), what is the sum for n = 12?The sum of 1/(k(k + 1)) for k = 1 to n is n/(n + 1). What is it for n = 9?For every natural n, 7^n - 1 is divisible by which number?What is the least n from which n! > 2^n holds for all larger n too?For 2^n >= n + 5, which base case value of n is used?In prefix induction, a number's prefix is formed by doing what?Predecessor induction is an n-step loop; prefix induction matches what?Backward induction needs the statement proved for what kind of set?In the ladder metaphor, the base case corresponds to what?Mathematical induction is closely related to which computing idea?A teacher adds every whole number from 1 to 50. What total results?A pupil adds the first 20 odd numbers 1, 3, 5, and so on. Find the total.A tiler counts squares of side 1 to 12 and adds their areas. What is the total?With 4- and 5-dollar coins, every amount from what value upward can be formed?The cubes of 1 up to 8 are added together. What is the sum?Products of neighbours 1x2, 2x3, up to 9x10 are summed. What is the total?A telescoping series adds 1/(k(k + 1)) for k = 1 to 19. What is its value?A factorial overtakes 2^n for good from which value of n?Why can the coin proof not start at 11 dollars?Which divisor does n^3 + 2n always have, whatever the natural number n?Three consecutive whole numbers are multiplied. Their product always has what greatest divisor?Show by induction that 10^n + 3(4^(n+2)) + 5 has which greatest divisor?A number of the form 5^n - 1 is always a multiple of which greatest number?Powers of eight, reduced by one, are always divisible by which number?Which scholar used induction in 1575 to show the first n odd numbers sum to n^2?The expression n^5 - n is a multiple of which greatest number for every n?By induction, 3^(2n+2) - 8n - 9 is a multiple of which largest number?Cauchy first proved the AM-GM inequality for which numbers of terms?Verify that 2(7^n) + 3(5^n) - 5 always divides evenly by which number?A doubling series runs 1, 2, 4, 8, up to 512. What is its total?A tripling series reads 1, 3, 9, 27, 81, 243. What does it add up to?A series begins 2, 6, 18, 54, 162. What is the sum of these five terms?Add the Fibonacci terms 1, 1, 2, 3, 5, 8, 13, 21. What is the total?Evaluate 1(1!) + 2(2!) + 3(3!) + 4(4!) using a factorial identity.How many subsets can be formed from a set holding 7 elements?A Tower of Hanoi puzzle has 6 disks. What is the fewest moves needed?Odd-product fractions 1/(1x3), 1/(3x5), up to 1/(19x21) are summed. Value?Induction over a set of ordinal numbers is given which name?A builder adds the squares of the odd numbers 1, 3, 5, 7, 9. Find the sum.Halving repeatedly gives 1/2, 1/4, 1/8, 1/16, 1/32, 1/64. What do they add to?Sum the triple products 1x2x3, 2x3x4, and so on up to 6x7x8.Moving a sum 1 + 2 + ... + n from k terms to k + 1 terms, which term joins?The step from P(k) to P(k + 1) is proved, but P(1) is false. What follows?A claim is to be proved for all n >= 3. What is the base case?In Peano's axioms, the successor of a natural number x is which?If natural numbers are taken to begin at 1, the base case uses which value?The flawed horse argument claims that all horses are what?Which pair of tools finishes the step for |sin nx| <= n|sin x|?