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Sequences, Series and Progressions

Find n if n C...

Question

Find n if ⁿC₈ = ⁿC₅

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Solution

∴n = 13

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a =^{n} C_{0} +^{n} C_{3} +^{n} C_{6} + . . .

b =^{n} C_{1} +^{n} C_{2} +^{n} C_{4} +^{n} C_{5} +^{n} C_{7} +^{n} C_{8} + . . .

c =^{n} C_{1} -^{n} C_{2} +^{n} C_{4} -^{n} C_{5} +^{n} C_{7} -^{n} C_{8} + . . .

,
then the value of

{(a - \frac{b}{2})}^{2} + \frac{3 c^{2}}{4}

a =^{n} C_{0} +^{n} C_{3} +^{n} C_{6} + . . .

b =^{n} C_{1} +^{n} C_{2} +^{n} C_{4} +^{n} C_{5} +^{n} C_{7} +^{n} C_{8} + . . .

c =^{n} C_{1} -^{n} C_{2} +^{n} C_{4} -^{n} C_{5} +^{n} C_{7} -^{n} C_{8} + . . .

,
then the value of

{(a - \frac{b}{2})}^{2} + \frac{3 c^{2}}{4}

^{n} C_{8} =^{n} C_{2}

n

Q. If ⁿC₁₂ = ⁿC₅, find the value of n.

^{n} C_{3} =^{n} C_{5^{'}}

then find the value of n:

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