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Syllabus

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

7 + 77 + 777 + ....+ 777...(n digits)...7 = 7/81 (10^(n+1) - 9n - 10)

Prove by mathematical induction.

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

Prove that n

^{2}+ n is even , where n is natural number.?sinx + sin3x + ..............+ sin(2n-1)x = sin^2 nx / sinx

prove by PMI

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

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

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

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

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

^{5}/5+n^{3}/3+7n/15 is a natural number by using the principle of mathematical induction.Prove that 11

^{n+2 }+ 12^{2n+1 }is divisible by 133 for all n belongs to N .p(n) =1+4+7+...+(3n-2)=1/2n(3n-1)

P.T by principle of mathematical induction

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

prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nENProve 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

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.....using principle of mathematical induction prove that, 1

^{2}+ 2^{2}+....+ n^{2}(n^{3}/3) for all n belonging to natural numbersby mathematical induction prove that :

x

^{2n-1} -1 is divisible by x-1Prove 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??using mathematical induction

prove that

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

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

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

2+7+12+...+(5n-3)=n(5n-1)/2

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: 5

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

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

If P(n) is the statement “2

^{n}> 3n” and if P(k) is true, show that p(k+1) is also true .1+4+7+---------+(3n-2)=

1n(3n-1)2

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

Find the multiplicative inverse of (6+5i)

^{2}what is principle of mathamatical induction

Prove , by mathematical induction , that 5

^{n+1}+4.6^{n}when divided by 20 leaves remainder 9 for all nProve by induction that (2n+7)<(n+3)

^{2}is true7 divides 2

^{3n}-1in 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.^{2n-1}+ 1 is divisible by 16 .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}).Using the principle of mathematical induction, prove for n belonging to N:

(2^3n - 1) is divisible by 7

using mathematical induction prove that

n(n+1)(n+2) is divisible by 6.1/1.2 + 1/2.3 = 1/3.4 +.........+ 1/n(n+1 )= n/n+1 using principle of mathematical induction

X+ 4x + 7x + ….. (3n-2)x = 1/2n(3n-1)x .

7

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

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.

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

PROVE BY M.I (41)

^{n}-(14) is multiple of 27Prove the following by the PMI :

n7/ 7 + n5 / 5 + n3 / 3 + n2/ 2 - 37/210n is a positive integer for all n belongs to 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.

for every positive integer n.prove that 7

^{n}-3^{n}is divisible by 4prove the following by mathematical induction:- 10

^{2N-1}+1 IS DIVISIBLE BY 11