If-P-n-denotes-the-product-of-the-binomial-coefficients-in-the-expansion-of-1-x-n-then-P-n-1-P-n-equals- Tinku Tara June 14, 2023 None 0 Comments FacebookTweetPin Question Number 52600 by Tip Top last updated on 10/Jan/19 IfPndenotestheproductofthebinomialcoefficientsintheexpansionof(1+x)n,thenPn+1Pnequals Commented by Abdo msup. last updated on 10/Jan/19 wehave(x+1)n=∑k=0nCnkxk⇒Pn=∏k=0nCnk=Cno.Cn1…..Cnn⇒Pn+1=Cn+10.Cn+11…Cn+1n+1⇒Pn+1Pn=∏k=0nCnk∏k=0n+1Cn+1k=∏k=0nCnk∏k=0n(n+1)!k!(n+1−k)!=∏k=0nCnk∏k=0nn+1(n+1−k)∏k=0nn!k!(n−k)!=∏k=0n(n+1−k)n+1=(n+1)!(n+1)n+1=(n+1)n!(n+1)(n+1)n=n!(n+1)n. Answered by tanmay.chaudhury50@gmail.com last updated on 10/Jan/19 pn=nc0×nc1×nc2…ncn←productofntermspn+1=n+1c0×n+1c1×n+1c2..×n+1cn+1←productof(n+1)termsnowratioofr+1thterm=n+1crncr=(n+1)!r!(n+1−r)!n!r!(n−r)!=(n+1)!n!×(n−r)!(n+1−r)!=n+1n+1−rsopn+1pn.==n+1n+1−0×n+1n+1−1×n+1n+1−2…=(n+1)n(n+1)! Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: 81-1-4-9-3-2-27-4-3-Next Next post: 0-pi-2-log-sin-2x-dx- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.