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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 .
Prove that 2.7n + 3.5n - 5 is divisible by 24 for all n belongs to N. [ please explain with steps]
solve this equation :-
4k3+ 18k2 + 23k + 9 =0 (step by step)
Prove that x2n-y2n 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.
1.2 + 2.22+ 3.22+ … +n.2n= (n– 1) 2n+1+ 2
this 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 10n + 3.4n+2 + 5 is divisible by 9
Please 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?
find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1
Prove that 11n+2 + 122n+1 is divisible by 133 for all n belongs to N .
5+15+45+....+5.3n-1 = 5/2(3n-1)
Prove: 52n-1 is divisible by 24 for all n N
Using PMI, prove that
52n+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, 12 + 22 +....+ n2 (n3/3) for all n belonging to natural numbers
Q. 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 k3+6k2+9k+4??
Prove that 2.7n + 3.5n-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)
= 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.
using mathematical induction
7+ 77+ 777+ ..............+ 77.........7 = 7/81 (10to the power n+1 -9n-10)
P.T by 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 n2 + n is even , where n is natural number.?
3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)
Prove that (2n)! /22n(n!)2 <=1/in root whole 3n +1 for all n belonging to natural numbers by PMI.
1/2*5+ 1/5*8 + 1/8*11 +.......................+
n7/7 + n5/5 + 2n3/3 - n/105 is an integer , prove by PMI.
prove by ibduction that the sum Sn=n3+3n2+5n+3 is divisible by 3 for all nEN
Using the principle of mathematical induction, prove for n belonging to N:
(2^3n - 1) is divisible by 7
3^2n -1 is divisible by2^n+2 for all nN
By using principle of mathematical induction, prove that for all n element of N:
3^2n+2 - 8n - 9 is divisible by 64.
By s plitting 1.1 and then applying Binomial Theorem, the first few terms of (1.1) 10000 can be obtained as
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 200oC and 300oC.
11 power n+2 + 12 power 2n+1 is divisible by 133
Prove that 1/2 tan (x/2)+1/4tan(x/4)+...+(1/2n)tan (x/2n)=(1/2n)cot(x/2n) - cotx for all n (- N and 0<x<(pi/2).
Prove by induction that (2n+7)<(n+3)2is true
7 divides 23n-1
using mathematical induction prove that n(n+1)(n+2) is divisible by 6.
what is principle of mathamatical induction
prove that 41 n - 14 n is a multiple of 27.
7n-3n is a divisible by 4.
please solve this
In the above solved example how is = 9(k + 1) (8 + 1) − 8k − 8 − 9
= 8. 9(k + 1) + 9(k + 1) − 8k − 8 − 9
PROVE BY M.I (41)n-(14) is multiple of 27
FOR EVER POSITIVE INTEGER N POOVE THAT 7N-3N IS DIVISIBLE BY 4
SIR I DONT UNDERTAND FROM THE ABOVE SOLUTION AS U HAVE DONE ABOVE
PLS EXPLAIN THIS QUESION AGAIN
Prove the following by using the principle of mathematical induction for all
(2n+7) < (n+ 3)2
can any pls explain this question in detail??? cuz i can't get it
PMI help! test on sat!
example 6 of NCERT txt on pg 92!
how is 5k-5 a multiple of 4?
prove that 2n 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.
prove the following by mathematical induction:- 102N-1+1 IS DIVISIBLE BY 11
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