Question

9+1
Q. In an A. P, if the other term is 1/q+1 and qth term is
1/p+1,find the sum of the first (p+q) Terms​

Answer 1

tp=a+(p-1)d=1/(q+1)

tq=a+(q-1)d=1/(p+1)

tp-tq=(p+1-q-1)d=(q+1-p-1)/(p+1)(q+1)

d=1/(p+1)(q+1)

a+(p-1)/(p+1)(q+1)=1/(q+1)

a=1/(q+1)-(p-1)/(p+1)(q+1)

=(p+1-p+1)/(p+1)(q+1)

=2/(p+1)(q+1)

sp+q=(p+q)/2{2*2/(p+1)(q+1)+(p+q-1)/(p+1)(q+1)

=(p+q)/2{4+p+q-1)/(p+1)(q+1)

(p+q)(p+q+3)/2(p+1)(q+1)