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Prove that a+(a+d)+(a+2d)+........n "ter...

Prove that `a+(a+d)+(a+2d)+........n "terms"=n/2(2a+(n-1)d)`

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Using Mathematical induction. For all n in N . Show that a+(a+d)+(a+2d)+…………..n "upto n terms" = n/2 [2a+(n-1)d] .

Prove that a+ar+ar^2+.......+n "terms" =(a(r^n+1))/(r-1),r ne 1

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Using the principle of finite Mathematical Induction prove that 1^2+(1^2+2^2)+(1^2+2^2+3^2)+.......n terms =(n(n+1)^2(n+2))/12,foralln in N

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Prove that sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)

Using the principle of M.I, prove that 4^3+8^3+12^3 + ……… n terms = 16n^2(n+1)^2

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SRISIRI PUBLICATION-MATHEMATICAL INDUCTION -LONG ANSWER QUESTIONS
  1. Using the principle of finite Mathematical Induction prove that 1.2.3+...

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  2. Using the principle of Mathematical Induction , forall n in N, prove t...

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  3. Show that 2+7+12……….+(5n-3)= (n(5n-1))/2

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  4. Using the principle of finite Mathematical Induction prove that 1^2+(1...

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  5. Show that 1/1.3+1/3.5+1/5.7+..........+n "terms"=n/(2n+1)

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  6. Show that 1^3/1+(1^3+2^3)/(1+3)+............n "terms "=n/24(2n^2+9n+13...

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  7. Prove that a+ar+ar^2+.......+n "terms" =(a(r^n+1))/(r-1),r ne 1

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  8. Prove that a+(a+d)+(a+2d)+........n "terms"=n/2(2a+(n-1)d)

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  9. By mathematical induction, show that 49^n+16n-1 is divisible by 64 fo...

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  10. Using the principle of Mathematical Induction, show that 2.4^(2n+1)+3^...

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  11. Prove that x^n-y^n is divisible by x - y for all positive integers n.

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  12. Prove that x^m+y^m is divisible by x + y, when m is an odd natural nu...

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  13. Using the principle of finite Mathematical Induction prove the followi...

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  14. Using the principle of M.I, prove that 4^3+8^3+12^3+ ……… n terms =16n^...

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  15. Use mathematical induction to prove that statement sum(k = 1)^(n) (2 ...

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  16. Using Mathematical Induction, prove that statement for all n in N (1...

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  17. Prove that: 1^2+2^2+3^2++n^2>(n^3)/3 for all""n in Ndot

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  18. Use Mathematical induction to prove that (1 + x)^(n) gt 1 + nx for n ...

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  19. Use mathematical induction to prove that 2 n - 3 le 2^(n-2) for all n...

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