(iv) (a + b) के प्रसार में मध्य पद क्या होगा, जबकि n सम संख्या है?
(v) sinr=0है तब का मान क्या होगा?
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Given : (a + b)^n के प्रसार , n सम संख्या
To Find : मध्य पद
Solution:
( a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +......................+ ⁿCₙ₋₁a¹bⁿ⁻¹ + ⁿCₙa⁰bⁿ
n सम संख्या है
n = 2x
( a + b)²ˣ
= ²ˣC₀a²ˣb⁰ + ²ˣC₁a²ˣ⁻¹b¹ + ²ˣC₂a²ˣ⁻²b² +..................+ ²ˣC₂ₓ₋₁a¹b²ˣ⁻¹ + ⁿC₂ₓa⁰b²ˣ
2x + 1 पद
मध्य पद = x + 1 पद
x + 1 पद = ²ˣCₓaˣbˣ
मध्य पद = ²ˣCₓaˣbˣ
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