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Syllabus

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

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

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

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

7 divides 2

^{3n}-1prove by using PMI that 4 raise to n + 15n - 1 is divisible by 9 .

Prove that x

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

Prove: 5

^{2n}-1 is divisible by 24 for all n NProve 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.

by mathematical induction prove that :

x

^{2n-1} -1 is divisible by x-1Prove that n(n+1)(n+2) is divisible by 6

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

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

using induction, prove that 10

^{n }+ 3.4^{n+2}+ 5 is divisible by 9^{k}-5 is divisible by 4 by principle of mathematical induction^{2n}+ 2^{3n-3}, 3^{n-1}is divisible by 25, for all n Ꜫ N.5+15+45....+5.3

^{n-1}= 5/2(3^{n-1})Prove that 11

^{n+2 }+ 12^{2n+1 }is divisible by 133 for all n belongs to N .find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1

^{n+1}- 9n - 10)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

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

using principle of mathematical induction prove that, 1

^{2}+ 2^{2}+....+ n^{2}(n^{3}/3) for all n belonging to natural numbersProve that n

^{2}+ n is even , where n is natural number.?Q. Prove that 1.3+2.4+3.5+....+n(n+2) = 1/6n (n+1) (2n+7),

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

^{3}+6k^{2}+9k+4??Prove by induction:

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

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

using mathematical induction

prove that

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

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

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.

3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

prove that (1+x)

^{n}>=(1+nx),for all natural number n,where x>-1Hi

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

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

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

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

= n/6n+4

prove by PMI

Prove by PMI

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

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

1n(3n-1)2

prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nENin 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 by induction that (2n+7)<(n+3)

^{2}is trueProve 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}).what is principle of mathamatical induction

If P(n) is the statement “2

^{n}> 3n” and if P(k) is true, show that p(k+1) is also true .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 the following by mathematical induction:- 10

^{2N-1}+1 IS DIVISIBLE BY 11PROVE 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 by M.I that x + 4x + 7x +....+ (3n-2)x = 1/2n(3n-1)x