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State the principle of mathematical indu...

State the principle of mathematical induction.

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Using the principle of mathematical induction. Prove that (x^(n)-y^(n)) is divisible by (x-y) for all n in N .

Prove by the principle of mathematical induction that. 4^n+15n-1 is a mulitple of 9 for all n in N .

Prove by the principle of mathematical induction that when every even power of every odd integer greater than 1 is divided by 8, the remainder is always 1 .

Use the principle of mathematical induction to show that 5^(2+1)+3^(n+2).2^(n-1) divisible by 19 for all natural number n.

Prove the following by the principle of mathematical induction: \ 1. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Applying the principle of mathematical induction (P.M.I.) prove that 1^2+2^2+3^2+.......+n^2=(n(n+1)(2n+1))/6

Using the principle of mathematical induction prove that 41^n-14^n is a multiple of 27 .

If ninNN , then by principle of mathematical induction prove that, 10^(n)+3*4^(n+2)+5" "[nge0] is divisible by 9.

Using the principle of mathematical induction ,prove that x^n-y^n is divisible by (x-y) for all n in N .

If ninNN , then by principle of mathematical induction prove that, 5^(2n+2)-24n-25 is divisible by 576.

UNITED BOOK HOUSE-TIRTHAPATI INSTITUTION -EXERCISE
  1. Determine the modulus-amplitude form of the comples number (sqrt3+i)

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  2. If the sum of the two roots of the quadratic equation x^2-px+q=0be the...

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  3. State the principle of mathematical induction.

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  4. If AsubeBand BsubeCthen show that AsubeC.

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  5. Show that (cos2^@-sin2^@)/(cos2^@+sin2^@)=tan43^@

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  6. If x costheta+ysintheta=xcosphi+ysinphithen show that y=x tan ((theta+...

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  7. IF 2 costheta=x+1/xthen show that 2 cos3 theta=x^3+1/x^3

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  8. Find the value of sin (221//2^@) with the help of the value of cos45^@

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  9. tan25^@=a prove that (tan155^@-tan115^@)/(1+tan155^@.tan115^@)=(1-a^2)...

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  10. Prove that,cos(pi/5)-cos((2pi)/5)=1/2

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  11. By the principle of mathematical induction prove that (5^(2n)-1)is alw...

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  12. IF x=a+bw+cw^2,y=a+bw^2+cwthen show that x^3+y^3=(2a-b-c)(2b-c-a)(2c-a...

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  13. If the roots of the quadratic equation a(b-c)x^2+b(c-a)+c(a-b)=0be eq...

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  14. Prove that (AcupB)^c=A^c capB^c[without venn-diagram]

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  15. If sinx-siny=a and cosx+cosy=b,prove that tan((x+y)/2)=+-sqrt((4-a^2-b...

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  16. Mathematically find the value of sin18^@

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  17. Show that cos(pi/11)cos((2pi)/11)cos((3pi)/11)cos((4pi)/11)cos((5pi)/1...

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  18. If cosx+cosy+cosz=0and sinx+siny+sinz=0then show that cos(x-y)+cos(y-z...

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  19. If z=x+iy and |2z-1| =|z-2|then prove that x^2+y^2=1

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  20. If the two roots of the quadratic equation ax^2+bx+c=0and alphaand bet...

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