Call me

Have a Query? We will call you right away.

+91

E.g: 9876543210, 01112345678

We will give you a call shortly, Thank You

Office hours: 9:00 am to 9:00 pm IST (7 days a week)

What are you looking for?

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)

2^5n>3^3n for n belongs to natural no.

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

prove by PMI

5+15+45....+5.3

^{n-1}= 5/2(3^{n-1})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]

Prove that x

^{2n}-y^{2n}is divisible by x+y?solve this equation :-

4k

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

1.2 + 2.2

^{2}+ 3.2^{2}+ … +n.2^{n}= (n– 1) 2^{n}^{+1}+ 2this question is solved on this site...... but I can't understand how the final answer came ..... please see 4.1's 8th question on this site ......

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 9Please help me I can't solve questions of mathematical induction.I tried a lot but I always get confused in the (k+1)th step.Please tell what to do?

^{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 .Prove: 5

^{2n}-1 is divisible by 24 for all n N5+15+45+....+5.3

^{n-1}= 5/2(3^{n-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

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

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??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.....= 9

^{(}^{k}^{ + 1) }(8 + 1)= 8. 9

^{(}^{k}^{ + 1)}+ 9^{(}^{k}^{ + 1)}can anyone explain me 2 step how it came...please it is of example no 1.

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

P.T by principle of mathematical induction

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 + …….. + 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

^{3}- n is divisible by 6, for each natural number n >= 23.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

How does (k+2)(k+1) become P(k+1) in the video?

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

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

= n/6n+4

prove by PMI

Prove 2220

^{2n}^{+1}+2003^{2n+1}is divisible by 4005,nbelongs toNprove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nEN(X2n -1) is divisible by (X-1)

its actually X raise to the power 2n

Using the principal of mathematical induction, prove for n belonging to N:

n(n+1)(n+2) is a multiple of 6

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 that 2^n

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

1n(3n-1)2

Prove that the fractionis irreducible for every natural number.

Prove by PMI

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

there are total 50 ques in ex12.2 of r.d sharma, ch. mathematical induction

but meritnation has provided only solutions to 37 ques

certain ques are missing from in between

kindly rectify this problem.

regards

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

(1) 2ac = ab + bc (2) 2ab = ac + bc (3) 2b = a + c (4) b

^{2}= acProve 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 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.prove that 41

^{n}- 14^{n}is a multiple of 27.what is principle of mathamatical induction

7

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

prove by principal of mathmatical induction that:n

^{2}+n is an even natural numberPROVE BY M.I (41)

^{n}-(14) is multiple of 27Using the principle of mathematical induction, prove for n belonging to N:

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

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

3^2n -1 is divisible by2^n+2 for all nN

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.

By s plitting 1.1 and then applying Binomial Theorem, the first few terms of (1.1)

How the second term 11000 occurs instead of 1000^{10000 }can be obtained askindly clarify