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Syllabus

sinx+sin2x+sin3x+...+sin nx=sin((n+1)/2)x .((sin nx)/2) / sin(x/2)

Prove that 1.2 + 2.3 + 3.4 +..............n(n+1) = 1/3 n (n+1)(n+2)

prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nENsinx + sin3x + ..............+ sin(2n-1)x = sin^2 nx / sinx

prove by PMI

sin theta + sin 2 theta + sin 3 theta + .......+ sin n theta = [sin ( n + 1)/2 / sin 0/2 ] multiplyby sin n theta / sin 0 /2 dont be confused experts this question is related to pmi so clear my doubts by providing the solution of my query of exact question without providing any link.

prove by using PMI that 4 raise to n + 15n - 1 is divisible by 9 .

1^4+2^4+3^4+..........+n^4 =n(n+1)(2n+1)+(3n^2+3n-1)/30. (whole divided by 30)

Prove that 2.7n + 3.5n - 5 is divisible by 24 for all n belongs to N. [ please explain with steps]

Prove that x

^{2n}-y^{2n}is divisible by x+y?Prove that n(n+1)(n+5) is a multiple of 3

7 divides 2

^{3n}-1Using PMI Prove that 1^2 + 2^2 + ......... + n^2 n^3/3

Prove by PMI

1) a+(a+d)+(a+2d)+ ......[a+(n-1)d] = n/2 [2a+(n-1)d], n E N.

2) n(n+1)(n+5) is divisible by 6 for all n E N.

3) 9 raised to n - 8n - 1 is a multiple of 64 for all n E N.

3^4n+2 + 5^2n+1 is a multiple of 14

Prove that n(n+1)(n+2) is divisible by 6

1 sqare + 2 square + 3 square +.............+n square >n cube +3 . prove it by mathematical induction.

using induction, prove that 10

^{n }+ 3.4^{n+2}+ 5 is divisible by 9using principle of mathematical induction prove that, 1

^{2}+ 2^{2}+....+ n^{2}(n^{3}/3) for all n belonging to natural numbers^{2n}+ 2^{3n-3}, 3^{n-1}is divisible by 25, for all n Ꜫ N.find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1

Prove that 11

^{n+2 }+ 12^{2n+1 }is divisible by 133 for all n belongs to N .Prove: 5

^{2n}-1 is divisible by 24 for all n NUsing PMI, prove that

5

^{2n+2}-24n-25 is divisible by 576 for n belongs to N.Prove the following

1.3 + 3.5 + 5.7 + ..... +(2n - 1) (2n + 1 ) =n( 4n square + 6n -1)/2 plz explain briefly in a simple method

3

^{2n- 1}+ 3^{n}+4 is divisible by 2.Q. Prove that 1.3+2.4+3.5+....+n(n+2) = 1/6n (n+1) (2n+7),

~~V~~nEN.Prove that n

^{2}+ n is even , where n is natural number.?how to split a cubic polynomial like k

^{3}+6k^{2}+9k+4??prove that (1+x)

^{n}>=(1+nx),for all natural number n,where x>-1bY PMI prove n(n+1)(2n+1) is divisible by 6

Prove that 2.7

^{n}+ 3.5^{n}-5 is divisible by 24, for all n belongs to N....Plzzz dnt tell to refer textbook as frm dat also its not clear to me plzzzzzz answer it as soon as possible.....^{2n-1}+ 1 is divisible by 16 .Prove by induction:

1/1.2 + 1/2.3 + 1/3.4 + ..... to n terms = n/(n+1)

^{5}/5+n^{3}/3+7n/15 is a natural number by using the principle of mathematical induction.using mathematical induction

prove that

7+ 77+ 777+ ..............+ 77.........7 = 7/81 (10to the power n+1 -9n-10)

1 / 1.2.3 + 1 / 2.3.4 + 1 / 3.4.5 + …….. + 1 / n (n+1) (n+2) = n (n+3) / 4 (n+1) (n+2) ? using principle of mathematical induction prove the following for all n E N ?

^{k}-5 is divisible by 4 by principle of mathematical induction^{n-1}x) = sin 2^{x}a/ 2^{x}sin a3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

By Principle of Mathematical Induction, prove that:

12

^{n}+ 2.5^{n-1}is divisible by 7.

1/2*5+ 1/5*8 + 1/8*11 +.......................+

1/(3n-1)(3n+2)

= n/6n+4

prove by PMI

using the principles of mathematical induction prove that

(1+x)

^{n}> (1+nx) forall n belongs to N where x>-1????Hi

By using principle of mathematical induction, prove that for all n element of N:

3^2n+2 - 8n - 9 is divisible by 64.

1+4+7+---------+(3n-2)=

1n(3n-1)2

^{n}- 3^{n}is divisible by 4.Prove that, x

^{2n}- y^{2n}is divisible by x+y.by mathematical induction prove that :

x

^{2n-1} -1 is divisible by x-1in drilling worlds deepest hole it was found that the temperature T in degree celcius at x km below the surface of the earth was =30+25(x - 3), 3 less than x less than 15. at what depth will the temperature lie b/w 200

^{o}C and 300^{o}C.^{n-1}a) = sin 2^{n}a / 2^{n}sin aProve by PMI

n(n+1)(n+5) is divisible by 6 for all n belongs to natural numbers

11 power n+2 + 12 power 2n+1 is divisible by 133

Prove by induction that (2n+7)<(n+3)

^{2}is truewhat is P.M.I. this? EXPLAIN .

Prove that

^{ 1}/_{2 }tan (^{x}/_{2})+^{1}/_{4}tan(^{x}/_{4})+...+(^{1}/_{2n})tan (^{x}/_{2n})=(^{1}/_{2n})cot(^{x}/_{2}^{n}) - cotx for all n (- N and 0<x<(^{pi}/_{2}).How can we prove that :

(1 + 1 / 3) (1 + 5 / 4)(1 + 7 / 9)........{(1 + (2n + 1 / n

^{2})} = (n + 1)^{2 }for all n Є N.Please answer this question!!!!!!!!!!what is principle of mathamatical induction

using mathematical induction prove that

n(n+1)(n+2) is divisible by 6.7

^{n}-3^{n}is a divisible by 4.please solve this

PROVE BY M.I (41)

^{n}-(14) is multiple of 27Use mathematical induction to prove

sin x + sin 3x+ sin 5x +..............+sin(2n-1)x = (sin nx)^2)/sin x

Prove the following by using the principle of mathematical induction for all

(2

n+7) < (n+ 3)^{2 }can any pls explain this question in detail??? cuz i can't get it

Prove by mathematical induction that n(n+1) (2n+1) is a multiple of 6 for all n∈N

prove that 2

^{n}is greater than n for all positive integers n.this is example 2 from the ncert maths text book.

plzz...answer soon....i dint get the last step.