If 1- x 15- C 0- C 1 x - C 2 x 2- C 15 x 15- thenC 2-2 C 3-3 C 4- -14 C 15-A- 14-214B- 13-214-1C- 13-214-1D- None of these

The correct option is B (1+x)^15 c_0=x[c_1+c_2x+c_3x^2+–c_15x^14] ⇒(1+x)^15 c_0/x= c_1+c_2x+c_3x^2+–+c_15x^14 Diffrentiate both sides w.r.to 'x' and replac ...

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Byju's Answer

Standard XI

Mathematics

Differentiation to solve modified sum of binomial coefficients

If 1+ x 15= C...

Question

If $(1 + x)^{15}$ = $C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . . . . + C_{15} x^{15}$ , then

$C_{2} + 2 C_{3} + 3 C_{4} + . . . . . . . . + 14 C_{15}$ =

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None of these

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Solution

The correct option is B

$(1 + x)^{1} 5 - c_{0} = x [c_{1} + c_{2} x + c_{3} x^{2} + - - c_{15} x^{14}] \Rightarrow \frac{(1 + x)^{15} - c_{0}}{x} = c_{1} + c_{2} x + c_{3} x^{2} + - - + c_{1} 5 x^{1} 4 D i f f r e n t i a t e b o t h s i d e s w . r . t o^{'} x^{'} a n d r e p l a c e x = 1 ∴ {13.2}^{14} + 1 = c_{2} + 2 c_{3} + 3 c_{4} + - - + 14 c_{15}$

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Similar questions

Q. If

(1 + x)^{15} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . + C_{15} x^{15},

then

C_{2} + 2 C_{3} + 3 C_{4} + . . . . . . + 14 C_{15} =

Q. If

(1 + x)^{15} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . + C_{15} x^{15},

then

C_{2} + 2 C_{3} + 3 C_{4} + . . . . . . + 14 C_{15} =

Q. If

(1 + x)^{15} = C_{0} + C_{1} x + C_{2} x^{2} + \dots \dots + C_{15} x^{15},

find the value of

C_{2} + 2 C_{3} + 3 C_{4} + \dots \dots + 14 C_{15}

Q. If

f (x) = (1 + x)^{15} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{15} x^{15},

then

f (2) =

Q. If

{(1 + x)}^{15} = C_{0} + C_{1} . x + C_{2} . x^{2} + . . . . + C_{15} . x^{15}

and

C_{2} + 2 C_{3} + 3 C_{4} + . . . . + 14 C_{15} = a 2^{b} + c,

then find

a + b + c

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If (1+x)15 = C0+C1x+C2x2+.........+C15x15, then C2+2C3+3C4+........+14C15=

The correct option is B (1+x)15−c0=x[c1+c2x+c3x2+−−c15x14]⇒(1+x)15−c0x= c1+c2x+c3x2+−−+c15x14Diffrentiate both sides w.r.to ′x′ and replace x=1∴ 13.214+1=c2+2c3+3c4+−−+14c15

If $(1 + x)^{15}$ = $C_{0} + C_{1} x + C_{2} x^{2} + . . . . . . . . . + C_{15} x^{15}$ , then

$C_{2} + 2 C_{3} + 3 C_{4} + . . . . . . . . + 14 C_{15}$ =