CBSE Guess > Papers > Important Questions > Class XI > 2010 > Maths > Maths By Mr. Anil Kumar Tondak
CBSE CLASS XI
**Principle of Mathematical Induction**
Prove the followings by using Principle of Mathematical Induction:
** Q.1. **1 + .
**Q.2. **
**Q.3. **
**Q.4. ** 1 + 2 + 3 +-------+ n =
**Q.5 . **. 12 + 32 + 52 +-----------+(2n – 1)2 =
**Q.6. ** 1.3 + 2.4 + 3.5 +--------+n.(n+2) = 1/6 n(n+1)(2n+7)
**Q.7. **.
**Q.8. ** 1.2.3 + 2.3.4 + … + n (n + 1) (n+2) = for all n ÎN.
**Q.9. **
**Q.10. **
**Q.11. **
**Q.12.** 1 + 4 + 7 +-------+(3n-2) =
**Q.13.** 12 + 22 + 32 +---------+ to n term = .
**Q.14. ** 3.6 + 6.9 + 9.12 +--------+3n(3n+3) =3n (n+1) (n+2)
**Q.15. **
**Q.16. **
**Q.17. ** 1.3 + 2.32 + 3.32 + … + n.3n = for all n ÎN.
**Q.18. **a + ar + ar2+----------+arn-1=
**Q.19.** Prove : 102n-1 + 1 is divisible by 11.
**Q.20.** Prove : 2.7n + 3.5n – 5 is divisible by 24 for all n N
**Q.21. **Prove: is divisible by 9
**Q.22.** Prove: 52n – 1 is divisible by 24 for all n ÎN.
**Q.23.** Prove: 32n + 7 is divisible by 8 for all n ÎN.
**Q.24.** Prove: 52n+2 – 24n – 25 is divisible by 576 for all n ÎN.
**Q.25.** Prove: 72n + 23n – 3 , 3n-1 is divisible by 25 for all n ÎN.
**Q.26.** Prove: n3 + (n + 1)3 + (n – 2)3 is a multiple of 9
**Q.27.** Prove: 4n + 15n – 1 is divisible by 9.
**Q.28.** Prove: 23n – 1 is divisible by 7
**Q.29.** Prove: is divisible by 64 for every natural number n .
**Q.30.** Prove: 2.7n + 3.5n – 5 is divisible by 24 for all n ÎN.
**Q.31.** Prove: 11n + 2 + 122n + 1 is divisible by 133 for all n ÎN.
**Q.32.** Prove: x2n-1 + y2n-1 is divisible by x + y for all n ÎN.
**Q.33.** Prove : x2n-1 is divisible by (x – 1)
**Q.34.** Prove by mathematical induction that 41n – 14n is a multiple of 27.
**Q.35.** Prove : 1 + 2 + 3 … + n < for all n ÎN.
**Q.36 .**Prove: 12 + 22 +----------+n2 > , n N.
**Q.37.** Prove: 3n > n for all nN
**Q.38.** Prove the rule of exponents (ab)n = an bn
**Q.39.** Prove by the principle of mathematical induction that:
n (n+1) (2n+1) is divisible by 6 for all n Î N
**Q.40.** If then prove thatis divisible by for every natural number n.
**Q.41 .** Prove by induction that (2n + 7) < (n + 3)2 for all natural numbers n. Using this, prove by induction that (n + 3)2 £ 2n+3 for all n ÎN.
Paper By Mr. Anil Kumar Tondak
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Ph No.: 9811363962 |