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Syllabus

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

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

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

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

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

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

5+15+45....+5.3

^{n-1}= 5/2(3^{n-1})Prove that x

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

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 9bY PMI prove n(n+1)(2n+1) is divisible by 6

^{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 .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: 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

13. Prove that, 5

^{n}- 5 is divisible by 4 for all n $\in $ N.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}+ 16n -1 is divisible by 64 Prove by mathematical inductionProve 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)

^{5}/5+n^{3}/3+7n/15 is a natural number by using the principle of mathematical induction.1/2x5 + 1/5x8 + 1/8x11 + ....................+ 1/(3n-1)(3n+2) = n / 6n+4

prove by PMI

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.?^{n-1}a) = sin 2^{n}a / 2^{n}sin a3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

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

P.T by principle of mathematical induction

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

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

= n/6n+4

prove by PMI

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

prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nEN^{2n-1}+ 1 is divisible by 16 .Hi

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

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

Prove by PMI

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

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

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.9n - 8n -1 is a multiple of 8

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}).^{n-1}x) = sin 2^{x}a/ 2^{x}sin an

^{3}- n is divisible by 6, for each natural number n >= 2Prove by induction that (2n+7)<(n+3)

^{2}is true7 divides 2

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

n(n+1)(n+2) is divisible by 6.why do we apply mode to tan theta= m2-m1/1+m1m2 ? tan theta can itself get both positive and negative values. what is the use of this modulus? not also here but it has been applied to many other cases

what is principle of mathamatical induction

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.

7

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

PROVE BY M.I (41)

^{n}-(14) is multiple of 271. 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?

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 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.