Challenging Problems in Binomial Theorem- Special Hl Level Sums
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SPECIAL HL GRADE SUMS BINOMIAL THEOREM FROM: SRIRAMAN .IYER. HEAD, DEPT OF MATHEMATICS, IB PROGRAM, ADITYA BIRLA WORLD ACADEMY MUMBAI .INDIA EMAIL:[email protected]
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Difficult problems on BINOMIAL THEOREM . from Head, dept of Math-IB . Mumbai. India. email:[email protected]
Transcript of Challenging Problems in Binomial Theorem- Special Hl Level Sums
SPECIAL HL GRADE SUMS
BINOMIAL THEOREM
FROM: SRIRAMAN .IYER. HEAD, DEPT OF MATHEMATICS, IB PROGRAM, ADITYA BIRLA WORLD ACADEMY MUMBAI .INDIA EMAIL:[email protected]
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(1) (a) Find the approximate value of (2.01)9
to 3 decimal places using Binomial
theorem
(b) Find the 7th term from the expansion
of the term
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(2) Using binomial theorem simplify
a. (x + 1
𝑥 )n + (x +
1
𝑥 )-n
b.if(x) = (x + 1
𝑥 )n + (x +
1
𝑥 )-n, find f(-x)
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(3) If f(x) = (1+x)n, then
a.Prove that f(x) = 𝑛𝐶𝑖 𝑥𝑖𝑖=𝑛𝑖=0
b. Prove that f(1) = 𝑛𝐶𝑖 𝑖=𝑛𝑖=0
c.Find f’(x)
d.Find f’(x) using a similar notation of (a)
e. Find f’(1)
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(4) If f(x,y) = ( 𝑥
𝑦 +
𝑦
𝑥 )6 -(
𝑥
𝑦 -
𝑦
𝑥 )6
a. Find the value of f(1,-1) using binomial
expansion
b.Does the expansion has an
independent term?. If yes, find
C.Find the sum of coefficients of 𝑥𝑚
𝑦𝑛 and
𝑦𝑛
𝑦𝑚 if
(i) m = n
(ii) m ≠ n
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(5) In the expansion of ( 1+x+2x2) ( 2x2- 1/3x)9
a. Find the 7th term
b.Find the coefficient of x3
c.Find the independent term if possible
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(6) (a)Expand [∛2 + 1
∛2 ]3 - [∜2 +
1
∜2 ]4
(b)find the approximate value of (a) in one
d.p
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(7) (a) Find the ratio of tn+1 and tn in the
expansion of (x+y)20
(b) Find the value of (a) when n=18
(c) Find the greatest term in the
expansion of (x+y)2 0 when x =1
and y = 2
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(8) In the expansion of [ x + 2
𝑥2 ]20
a. Find the middle term in the expansion
b.Find the sum of coefficients of fourth
term from the beginning and fourth term
from the last
c. Does independent term exist? Justify
d.If f(x) = [ x + 2
𝑥2 ]20, find f(-x)
e. Find f’(x) at x= 1.
f. If (1,a) satisfies the curve f(x) find the
value of “a”
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(9) (a)Find the coefficient of (1/x) in the
expansion of (1+x)n . ( 1+1/x)n
(b) if f(x) = (1+x)n . ( 1+1/x)n, f’(x)
(c) Prove that f(x) is a square function
when n =2
(d) If (2,b) satisfies the curve at n=5, find
the value of “b”
SPECIAL HL SUMS BINOMIAL THEOREM [email protected]
(10) Find the independent term of the
following expansion
a. [ √𝑥
3 +
√3
2𝑥2 ]10
b.if f(x) = [ √𝑥
3 +
√3
2𝑥2 ]10 find the middle
term in the expansion of f(x2)
c.Find the value of f(√3) of the 7th term
from the last when (a) is expanded
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