If a1, a2, ..., an are in A.P. and a1=0, then the value of (a3+a3a4+…+an−1an)−a2(a21+a31+…+an−21) is equal to
Explanation
a1=0⇒a2=d,a3=2d,…,an=(n−1)d
(<br>(a2a3)+(a3a4)+⋯+(an−1an)<br>)<br>−a2(<br>(a21)+(a31)+⋯+(an−21)<br>)
=<br>(<br>(12)+(23)+⋯+(n−2n−1)<br>)<br>−<br>(<br>(11)+(21)+⋯+(n−31)<br>)
=1+1+⋯+1+(n−2n−1)
=(n−3)+(n−1)
=2n−4
=(n−2)+(1n−2)
Explanation
a1=0⇒a2=d,a3=2d,…,an=(n−1)d
(<br>(a2a3)+(a3a4)+⋯+(an−1an)<br>)<br>−a2(<br>(a21)+(a31)+⋯+(an−21)<br>)
=<br>(<br>(12)+(23)+⋯+(n−2n−1)<br>)<br>−<br>(<br>(11)+(21)+⋯+(n−31)<br>)
=1+1+⋯+1+(n−2n−1)
=(n−3)+(n−1)
=2n−4
=(n−2)+(1n−2)
