Question

# The value of 19∑r=120Cr+1⋅(−1)r22r+1 is

A
2((34)20+4)
B
2((34)20+4)
C
2((34)204)
D
2((34)204)

Solution

## The correct option is B −2((34)20+4)19∑r=120Cr+1⋅(−1)r22r+1 =1219∑r=1 20Cr+1⋅(−14)r =1220∑r=2 20Cr⋅(−14)r−1 =−220∑r=220Cr⋅(−14)r =−2[(1−14)20−(20C0(−14)0+20C1(−14)1)] =−2((34)20+4)  Mathematics

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