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

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

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

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

Prove that 5^(n) (1+(n)/(5) +(n(n-1))/(5*10) +(n(n-1)(n-2))/(5*10*15)+…oo)=3^(n) (1+(n)/(2)+(n(n+1))/(2*4)+(n(n+1)(n+2))/(2*4*6)+…oo)

Show that Lt_(ntooo)(3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=-20/7

If n is integer greater than 1 show that a -^n C_1 (a - 1) +^n C_2(a-2) +^n C_3 (a- 3) ……+(-1)^n(a - n) = 0

Show that (2^(2) *C_(0) )/(1*2)+(2^(3)*C_(1))/(2*3)+(2^(4) *C_(2))/(3*4)+…+(2^(n+2)*C_(n))/((n+1)(n+2)) = (3^(n+2) - 2n-5)/((n+1)(n+2)) Hence deduce that (C_(0))/(1.2) -(C_(1))/(2.3) +(C_(2))/(3.4) -…=(1)/(n+2)

With usual notations prove that 2.C_0 + 7.C_1 + 12.C_2 + ……..+(5n + 2).C_n = (5n + 4).2^(n-1)

Prove that (1)/(1!(n-1)!) + (1)/(3!(n-3)!)+ (1)/(5!(n-5)!) + …….= (2^(n-1))/(n!)

Prove that 5.C_(0) +5^(2).(C_(1))/(2) +5^(3).(C_(2))/(3)+…+5^(n+1).(C_(n))/(n+1)=(6^(n+1)-1)/(n+1) Hence show that 5.C_(0) +(5^(2))/(2).C_(1)+(5^(3))/(3).C_(2)+….+(5^(11))/(11).C_(10)=(6^(11)-1)/(11)

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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