Given function is f(y)=1−(y−1)+(y−1)2−(y−1)3+........−(y−1)17 In the expansion of (y−1)n Tr+1=nCryn−r(−1)r coeff of y2 in (y−1)2=2C0 coeff of y2 in (y−1)3=−3C1 coeff of y2 in (y−1)4=4C2 So, coeff of termwise is 2C0+3C1+4C2+5C3+.........+17C15 =1+3C1+4C2+5C3+.........+17C15 =(3C0+3C1)+4C2+5C3+.........+17C15 =4C1+4C2+5C3+.........+17C15 =5C2+5C3+.........+17C15 =18C15=18C3