Question
If the coefficients of pth, (p+1)th and (p+2)th terms in the expansion of (1+x)n are in A.P., then
Answer: Option B
:
B
2ncp=ncp−1+pcp+1⇒2(n−p)!P!=1(n−p+1)!(p−1)!+1(n−p−1)!(p+1)!⇒2(n−p)p=1(n−p+1)(n−p)+1(p+1)ponsimplifingwegetn2−n(4p+1)+4p2−2=0
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:
B
2ncp=ncp−1+pcp+1⇒2(n−p)!P!=1(n−p+1)!(p−1)!+1(n−p−1)!(p+1)!⇒2(n−p)p=1(n−p+1)(n−p)+1(p+1)ponsimplifingwegetn2−n(4p+1)+4p2−2=0
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