RD SHARMA Solutions for Class 11-science Maths Chapter 12 - Mathematical Induction
Chapter 12 - Mathematical Induction Exercise Ex. 12.1
Chapter 12 - Mathematical Induction Exercise Ex. 12.2





for all nN
Prove by the principle of mathematical induction
n3 - 7n + 3 is divisible by 3 for all n Î N
Prove by the principle of mathematical induction
1 + 2 + 22 +…. + 2n = 2n + 1 -1 for all n Î N
Prove by the principle of mathematical induction
Prove that
cos a + cos (a + b) + cos (a + 2b) + …..+ cos (a + (n - 1)b)
Prove that the number of subsets of a set containing n distinct elements is 2n for all n Î N.
A sequence a1, a2, a3, …….. is defined by letting a1 = 3 and ak = 7 ak-1 for all natural numbers k ³ 2. Show that an = 3.7n-1 for all n Î N.
A sequence x0, x1, x2, x3, ……. is defined by letting x0 = 5 and xk = 4 + xk -1 for all natural number k. show that xn = 5 + 4n for all n Î N using mathematical induction.
Using principle of mathematical induction prove that
The distributive law from algebra states that for all real numbers c, a1 and a2, we have c (a1 + a2) = ca1 + ca2
Use this law and mathematical induction to prove that, for all natural numbers, n ³ 2, if c (a1 + a2 + …. + an) = ca1 + ca2 + …+ can.
Chapter 12 - Mathematical Induction Exercise Ex. 12VSAQ
State the first principle of mathematical induction.
Write the set of value of n for which the statement P(n):2n
N-{1,2,3} Where N is the set of all natural numbers
State the second principle of mathematical induction.
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