The value of -C115+2·C215-3·C315+…-15·C1515+C114+C314+C514+…+C1114 is
214
213-13
216-1
213-14
Explanation for the correct option:
Given, -C115+2·C215-3·C315+…-15·C1515+C114+C314+C514+…+C1114
Let,S1=-C115+2·C215-3·C315+…-15·C1515=∑r=115-1r·r·Cr15=15·∑r=115-1rCr-114[∵Crn=nrCr-1n-1]=15-C014+C114-C214+…-C1414(1-x)14=C014-C114x+C214x2-…+C1414x14=150=0
Let,S2=C114+C314+C514+…+C1114=C114+C314+C514+…+C1114+C1314-C1314=214-1-C1314[∵C1n+C3n+C5n+.....=2n-1]=213-14
So, S1+S2=0+213-14=213-14
Therefore, -C115+2·C215-3·C315+…-15·C1515+C114+C314+C514+…+C1114=213-14
Hence, option D is correct.