Question

(ii) Which term is the numerically greatest term in the expansion of (2x + 5y)34, when x = 3 & y = 2?
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Answer 1

$\huge \star\mathcal\orange{ᴀɴsᴡᴇʀ}$

Let T

r+1

be the greatest term in the expansion of(2x+3y)

34

Given:x=3,y=2

(2x+3y)

34

=(2x)

34

(1+

2x

5y

)

34

Take α=

2x

5y

⇒(2x+3y)

34

=(2x)

34

(1+α)

34

When x=3,y=2 then α=

2x

5y

=

2×3

5×2

=

3

5

Now,

∣α∣+1

(n+1)∣α∣

=

∣

∣

∣

∣

∣

3

5

∣

∣

∣

∣

∣

+1

(34+1)×

∣

∣

∣

∣

∣

3

5

∣

∣

∣

∣

∣

=

3

5

+1

35×

3

5

=

8

175

=21.875=22(approx) which is not an integer.

Hence,22nd term is the numerically greatest term.

Answer 2

(2×3)+(5×2)×34

6+10×34

16×34

544

Answer is 544