If the pth and qth term of an A.P are 1/q and 1/p rly. show that the sum of pq term is (pq/2+1/2)
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Ap=1/q
a+(p-1)d=1/q
a+pd-d=1/q. 1
Aq=1/p
a+(q-1)d=1/p
a+qd-d=1/p. 2
1-2
(p-q)d=1/q-1/p
(p-q)d=p-q/pq
d=1/pq
Putting d=1/pq in eq. 1
a+p(1/pq)-1/pq=1/q
a+1/q-1/pq=1/q
a=1/pq
Spq=pq/2(2/pq+{pq-1}1/pq)
Spq=pq/2(2/pq+pq/pq-1/pq)
Spq=pq/2(1/pq+1)
Spq=pq/2(1+pq/pq)
Spq=1/2(1+pq)
Spq=1/2+pq/2
a+(p-1)d=1/q
a+pd-d=1/q. 1
Aq=1/p
a+(q-1)d=1/p
a+qd-d=1/p. 2
1-2
(p-q)d=1/q-1/p
(p-q)d=p-q/pq
d=1/pq
Putting d=1/pq in eq. 1
a+p(1/pq)-1/pq=1/q
a+1/q-1/pq=1/q
a=1/pq
Spq=pq/2(2/pq+{pq-1}1/pq)
Spq=pq/2(2/pq+pq/pq-1/pq)
Spq=pq/2(1/pq+1)
Spq=pq/2(1+pq/pq)
Spq=1/2(1+pq)
Spq=1/2+pq/2
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yes he or she is right
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