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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)

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

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

prove by PMI

prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nENprove by using PMI that 4 raise to n + 15n - 1 is divisible by 9 .

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

Prove that n(n+1)(n+5) is a multiple of 3

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 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.

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

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

1. two classes meet at the same hr.

2. two classes meet at different hrs. and 30 students are enrolled in both the courses

3. what value is shown here?

using principle of mathematical induction prove that, 1

^{2}+ 2^{2}+....+ n^{2}(n^{3}/3) for all n belonging to natural numbersusing induction, prove that 10

^{n }+ 3.4^{n+2}+ 5 is divisible by 9^{2n-1}+ 1 is divisible by 16 .^{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

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

Q. Prove that 1.3+2.4+3.5+....+n(n+2) = 1/6n (n+1) (2n+7),

~~V~~nEN.how to split a cubic polynomial like k

^{3}+6k^{2}+9k+4??^{n-1}x) = sin 2^{x}a/ 2^{x}sin abY PMI prove n(n+1)(2n+1) is divisible by 6

7 divides 2

^{3n}-1Prove 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.....prove that (1+x)

^{n}>=(1+nx),for all natural number n,where x>-1Prove by induction:

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

Prove that n

^{2}+ n is even , where n is natural number.?^{5}/5+n^{3}/3+7n/15 is a natural number by using the principle of mathematical induction.what is P.M.I. this? EXPLAIN .

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 ?

If P(n) is the statement “2

^{n}> 3n” and if P(k) is true, show that p(k+1) is also true .3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

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

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

= n/6n+4

prove by PMI

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.in 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.using the principles of mathematical induction prove that

(1+x)

^{n}> (1+nx) forall n belongs to N where x>-1????Prove 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 trueBy Principle of Mathematical Induction, prove that:

12

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

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})._{1 = }1/2(a_{0}+ A/a_{0 }),a_{2 }= 1/2 (a_{1}+A/a_{1}) and a_{n}_{+1} =1/2(a_{n}+A/a_{n}) for n greater than or equal to 2,where a>0,A>0prove that

(an - root of A)/(an +root of A) = {(a1 - root of A)/(a1 + root of A)} 2n-1

what is principle of mathamatical induction

using mathematical induction prove that

n(n+1)(n+2) is divisible by 6.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!!!!!!!!!!^{k}-5 is divisible by 4 by principle of mathematical induction7

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

PROVE BY M.I (41)

^{n}-(14) is multiple of 27Prove 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 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.