Miscellaneous Examples (NCERT): Part 3 Video Lecture | Mathematics for Airmen Group X - Airforce X Y / Indian Navy SSR

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before watching this video you should
have watched my novel zero part 1 - part
15 in this example we are told that the
sum or position of the first three terms
sum of cohesion to first three terms of
expansion this is pipeline that is for T
1 plus T 2 plus T 3 is equal to 5 pi so
we know that TR plus 1 or this equation
will be 2 M + power M MCR minus 3 PI X
square to the power R into H to the
power n that will be something like this
MCR
minus 3 to the power R into X to the
power M minus 3 are clear because M
minus R here we have and here we have
two are a ministry on the coefficient is
this choice of T of 0 plus 1 plus T of 1
plus 1 plus T of T plus 1 why we have
done this because t of r plus 1 we know
so one against it 0 plus 1 is equal to 5
5 or R is between 0 this becomes M C 0
minus 3 to the power 0 r is equal to 1
this becomes M C 1 minus 3 to the power
1 in R is equal to 2 this becomes M C 2
minus 3 to the power
two MCS will is equal to 1 minus e to
the power 0 is also 1 MC 1 is 3 so are
the MC 1 is M and minus T to power 1 is
3 plus become minus this is minus so
this mm into 3 the last MC 2 is nothing
but M into M minus 1 by and minus 3
square is like why I am C 2 is minus M
into M s number 2 you know the MC 2 is
nothing but M factorial by 2 factorial M
into M minus 2 here so M mod M factor we
can also say n factorial is equal to M
into M minus 1 into M minus 2 p.m. we
can say and you can cancel in factorial
so what we got is M into M minus 1 by 2
factorial and 2pi traders are thing but
2 into 1 the two stream regardless so we
solve this equation this is equal to 5 5
or what we get then you solve this this
guy becomes 2 minus 6 M 2 common plus 9
M square minus 9 m is equal to 5 5 9 few
satirizes so what you get 9 M square
minus 15 M minus B this is equal to 5 5
8 this is what you get if you solve this
equation you get M is equal to this is
the value so we have found the value of
M now we have to find that term
containing expression actually
you use this formula this formula will
use we have we use formula and let me
use the space only so T of R plus 1 is
equal to MC R minus 3 to the power R in
X to the power M minus 3 R so we are
saying M minus 3 R is equal to 3 and M
is equal to t1 or e1 minus 3 R is equal
to 3 or R is going to 12 minus 3 is 9 9
by 3 is bundle so the coefficient we are
looking is M is 250 M is 2m C R is equal
to 3 because we put our zero to 3 we get
the value of hey this becomes H to the
power 3 so 12 C 3 minus 3 to the power 3
this is the value we're looking for
because we are doing 4 m CR minus u the
power on and R is equal to 3 here so by
putting our level 2 3 we get 2 LC 3 M is
equal to 12 this guy becomes 2 then
comes 3 this is 3 here so it is 12 Z 3
minus 3 to the power thing it's because
this also 12 minus 3 3 9 falou next part
3 and when you solve this we get minus 5
0 so that term is minus PI 9 hold 0 XP
what we have done here we went down that
the coefficient in the first 3 term is
equal to 5 5 9 so we have formed the co
efficient of the first 3 term we got the
value of M is going to be 2 L and then
we also found 4 TR plus 1 is equal to M
CR minus 3 power R 2 H to the power M
minus 3 R this is the equation we have
already derived now in this equation we
put M is equal to L and then we have
told at M minus 3 R is equal to 3
because here we have X to the power 3 so
we found the value of path our turned
out to be 3
by boot since we have know the value of
M and AH we just put the value of M and
R in this equation to get the value let
us take home example where we have to
find the value here we are told that P R
minus 5 and T 2 R minus 1 they are equal
no no they are not equal - the voice of
TR minus 5 is equal to 4 you for two
please note the question doesn't say
that these two are equal portions is the
coefficient of TR minus 5 is equal to
question of coefficient of T or minus 1
so first let's find P R minus 5 min T -
1 minus 1 1 1 plus X 1 so 4 1 plus X for
T of he is he going to do 34c he takes
to be born okay
monthly bar 34 minus K this we can
ignore is equal to 34 c t actually
partly this is 30k now
TR minus 5 we can also write t r minus 6
plus 1 this becomes K so this guy
coefficient I am talking about now for
the whole term let's say now this
becomes 34 G of n minus 6 into X of R -
this is the T of R minus 5 dumb say T of
2 R minus 1 we can write 2 1 minus 2
plus 1 this is 2 R minus 1 this becomes
34 C 2 R minus 2 into H 3 bar to work -
this is TR plus -5 term and this is TR
minus UT commencement now we are told
that the coefficients are same that
means this part is equal to
so let's equate this or 34c on minus six
is equal to 34 c - r - so with this
equation when we have and C a is equal
to NC B so that means either a is equal
to B or a plus B is equal to n we know
this when we have n C is equal to n CP
we have learned in the Google chapter of
combination then is equal to B or a +
visible to them here similarly here we
can see our minus 6 is equal to 2 or
minus 3 or our minus 6 plus 2 or minus 2
is equal to 13 let's solve this equation
so from this equation we get R is equal
to minus 6 plus 2 is equal to minus 1
and from this equation we get 3 R is
equal to 13 4 plus 8 is 11 42 or odd
since we know our can't be negative so
we discard this so R is going to 14 is
them what we have done here we were told
that coefficient of R minus 5 terms and
2 or minus 5 term of this equation y
equal so we have found these two terms
and then we have found the coefficient
of the shoot-down
we have and equate these two terms
cohesion and you give you this formula
if NC has got two LCP agree is good to
be your a plus B is equal to n and we
found two value of R 1 value comes out
to be negative so we discovered that
because our can't be negative and we
have taken files will be thank you
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