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Recent questions tagged exercise-4.1
Questions
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ (2n+7) < (n+3)^2$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q24
asked
May 1, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ 41^n-14^n$ is a multiple of 27.
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q23
asked
May 1, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ 3^{2n+2}-8n-9$ is divisible by 8.
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q22
asked
May 1, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ x^{2n}-y^{2n}$ is divisible by $x+y$.
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q21
asked
May 1, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ 10^{2n-1}+1$ is divisible by 11.
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q20
asked
May 1, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all n ∈ N: \[\] $ n(n+1)(n+5) $ is a multiple of 3.
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q19
asked
May 1, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all n ∈ N: \[\] $1+2+3+...+n<\large\frac{1}{8}$$(2n+1)^2$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q18
asked
May 1, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ \large\frac{1}{3.5}$$+\large\frac{1}{5.7}$$+\large\frac{1}{7.9}$$+...+\large\frac{1}{(2n+1)(2n+3)}$$=\large\frac{n}{3(2n+3)}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q17
asked
Apr 30, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ \large\frac{1}{1.4}$$+\large\frac{1}{4.7}$$+\large\frac{1}{7.10}$$+...+\large\frac{1}{(3n-2)(3n+1)}$$=\large\frac{n}{(3n+1)}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q16
asked
Apr 30, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ 1^2+3^2+5^2+...+(2n-1)^2=\large\frac{n(2n-1)(2n+1)}{3}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q15
asked
Apr 30, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ \bigg( 1+\large\frac{1}{1} \bigg)$$\bigg( 1+\large\frac{1}{2} \bigg)$$\bigg( 1+\large\frac{1}{3} \bigg)$$...\bigg( 1+\large\frac{1}{n} \bigg)$$=(n+1)$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q14
asked
Apr 30, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ \bigg( 1+ \large\frac{3}{1} \bigg)$$\bigg( 1+ \large\frac{5}{4} \bigg)$$\bigg( 1+ \large\frac{7}{9} \bigg)$$...\bigg( 1+ \large\frac{(2n+1)}{n^2} \bigg)$$=(n+1)^2$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q13
asked
Apr 30, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ a+ar+ar^2+...+ar^{n-1}=\large\frac{a(r^n-1)}{r-1}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q12
asked
Apr 30, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ \large\frac{1}{1.2.3}$$+\large\frac{1}{2.3.4}$$+\large\frac{1}{3.4.5}$$+...+\large\frac{1}{n(n+1)(n+2)}$$=\large\frac{n(n+3)}{4(n+1)(n+2)}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q11
asked
Apr 30, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ \large\frac{1}{2.5}$$+\large\frac{1}{5.8}$$+\large\frac{1}{8.11}$$+...+\large\frac{1}{(3n-1)(3n+2)}$$=\large\frac{1}{(6n+4)}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q10
asked
Apr 29, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $\large\frac{1}{2}$$+ \large\frac{1}{4}$$+\large\frac{1}{8}$$+...+\large\frac{1}{2^n}$$=1-\large\frac{1}{2^n}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q9
asked
Apr 29, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $1.2+2.2^2+3.2^2+...+n.2^n=(n-1)2^{n+1}+2$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q8
asked
Apr 29, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $1.3+3.5+5.7+...+(2n-1)(2n+1)= \large\frac{n(4n^2+6n-1)}{3}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q7
asked
Apr 29, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $1.2+2.3+3.4+...+n.(n+1) \bigg[ \large\frac{n(n+1)(n+2)}{3} \bigg]$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q6
asked
Apr 29, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $ n \in N $ \[\] $1.3+2.3^2+3.3^3+...+n.3^n=\large\frac{(2n-1)3^{n+1}+3}{4}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q5
asked
Apr 29, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $ n \in N $ \[\] $1.2.3 + 2.3.4+...+n(n+1)(n+2)= \large\frac{n(n+1)(n+2)(n+3)}{4}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q4
asked
Apr 29, 2014
by
thanvigandhi_1
1
answer
Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $1+ \large\frac{1}{(1+2)}$$+ \large\frac{1}{(1+2+3)}$$+...+ \large\frac{1}{(1+2+3...n)}$$= \large\frac{2n}{(n+1)}$
cbse
class11
ch4
mathematical-induction
bookproblem
sec3
exercise-4.1
q3
asked
Apr 29, 2014
by
thanvigandhi_1
1
answer
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