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Question

If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x)n are in A.P., then find the value of


Solution

Coefficients of the 2nd, 3rd and 4th term in the given expansion are:

nC1,nC2 and nC3

We have:

2×nC2=nC1+nC3

Dividing both sides by nC2, we get:

2=nC1nC2+nC3nC2

2=2n1+n23

6n6=6+n2+23n

n29n+14=0

n=7[n2 as 2 > 3 in the 4th term]


Mathematics
RD Sharma
Standard XI

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