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

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

prove by PMI

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

prove 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]

find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1

Prove that x

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

42) Find the equations of bisectors of the internal angles of the triangles, the equations of whose sides are x + 1 = 0, 3x - 4y - 5 = 0 and 5x + 12y - 27 = 0. Also, find the co-ordinates of incentre.

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.

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

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

using induction, prove that 10

^{n }+ 3.4^{n+2}+ 5 is divisible by 9^{2n}+ 2^{3n-3}, 3^{n-1}is divisible by 25, for all n Ꜫ N.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 Nby PMI prove , 1/1.3 + 1/3.5+ 1/5.7+.......... 1/(2n-1)(2n+1) = n/(2n+1)

Using 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

using principle of mathematical induction prove that, 1

^{2}+ 2^{2}+....+ n^{2}(n^{3}/3) for all n belonging to natural numbersQ. 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??^{2n-1}+ 1 is divisible by 16 .bY 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.....Prove by induction:

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

p(n) =1+4+7+...+(3n-2)=1/2n(3n-1)

P.T by principle of mathematical induction

^{5}/5+n^{3}/3+7n/15 is a natural number by using the principle of mathematical induction.13. Prove that, 5

^{n}- 5 is divisible by 4 for all n $\in $ N.5+15+45....+5.3

^{n-1}= 5/2(3^{n-1})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 + â€¦â€¦.. + 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 ?

Prove that n

^{2}+ n is even , where n is natural number.?Prove by using principle of mathematical induction :cos a+ cos (a+b)+ cos (a+2b)+......+cos [a+(n-1)b] = {cos [a+ ((n-1)/2)b]sin (nb/2)}/sin (b/2)

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

prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nENprove that the product of two consecutive natural numbers is an even umber using the principal of mathematical induction

Hi

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

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

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.

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

1n(3n-1)2

Prove by PMI

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

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

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 sq+2sq+3sq+4sq+......+n sq =n(n+1)(2n+1)/6.

please do the calculations in simplest way with details and please no links

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

^{2}is truesolve this equation :-

4k

^{3}+ 18k^{2}+ 23k + 9 =0 (step by step)7 divides 2

^{3n}-1using mathematical induction prove that

n(n+1)(n+2) is divisible by 6.for every positive integer n, prove that 7^n- 3^n is divisible by 4 plz expertz explain me how to solve dis step by step

what is principle of mathamatical induction

prove that 1x2 + 2x2^2 + 3x2^3+..+nx2^n = (n-1)x2^n+1 +2

7

^{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.