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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

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

Find the multiplicative inverse of (6+5i)

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

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.

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+2) is divisible by 6

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

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

1?+2?+3?+.+n?-[n(n+1)]?/2

using induction, prove that 10

^{n }+ 3.4^{n+2}+ 5 is divisible by 9Using PMI, prove that

5

^{2n+2}-24n-25 is divisible by 576 for n belongs to N.^{2n}+ 2^{3n-3}, 3^{n-1}is divisible by 25, for all n Ꜫ N.Q.11. Show that ${\mathrm{log}}_{2}\left[{\mathrm{log}}_{2}\left({\mathrm{log}}_{2}16\right)\right]=1$

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 N1/2x5 + 1/5x8 + 1/8x11 + ....................+ 1/(3n-1)(3n+2) = n / 6n+4

prove by PMI

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 numbersHow can we prove that :

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

^{2})} = (n + 1)^{2 }for all n Ð„ N.Please answer this question!!!!!!!!!!Q. Prove that 1.3+2.4+3.5+....+n(n+2) = 1/6n (n+1) (2n+7),

~~V~~nEN.Prove by induction:

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

how to split a cubic polynomial like k

^{3}+6k^{2}+9k+4??bY PMI prove n(n+1)(2n+1) is divisible by 6

^{n}= (A^{n})', where n belongs to N for any square matrix A.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.....^{5}/5+n^{3}/3+7n/15 is a natural number by using the principle of mathematical induction.Prove that n

^{2}+ n is even , where n is natural number.?^{k}-5 is divisible by 4 by principle of mathematical inductionusing 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 by induction that (2n+7)<(n+3)

^{2}is true3.6 +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

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

prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nEN1/3.5+1/5.7+1/7.9+ ...+1/(2n+1)(2n+3) =n/3(2n+3)

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

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}).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.

7 divides 2

^{3n}-1what is principle of mathamatical induction

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

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 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

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