Q1.12.2213+22.3213+23+32.4213+23+33+........ upto n terms is equal to
Answer : Option BExplaination / Solution:
Replace n = 1 we have 1/2. When n = 2 we have 1/2+1/6=2/3,( by the principle of mathematical induction when n = 1 we need to take one term from LHS. and for n = 2 we need to take the sum of two terms from the LHS. .....)
Q2.13.5+15.7+17.9+.......up to n terms is equal to
Answer : Option AExplaination / Solution:
By the process of mathematical induction when n = 1 we have 1/15. When n = 2 we have LHS : 1/15+1/35=2/21, RHS :2/(3(4+3))=2/21, which is true
Answer : Option AExplaination / Solution:
When n = 1 we get 64. When n = 2 we get 704 which is divisible by 64......... By the principle of mathematical induction it is divisible by 64.
Answer : Option AExplaination / Solution:
When n = 1 8<3, is not true. When n = 2 16<9, is false. When n = 3 32<27, is not valid. But when n = 4 64<81, is true.
Q7.The smallest positive integer for which The statement 3n+1<4n is true for
Answer : Option CExplaination / Solution:
When n = 1 9<4 not valid. when n = 2 27<16 not true. when n = 3 81<64 is in correct. when n = 4 243<256, is true.