If the sum of an AP is the same for p as for q terms, show that the sum for (p+q) terms is zero.
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Given:Sp=Sq
To prove : Sp+q=0
Formula: Sn=n/2 [2a+(n-1)d]
(copy the remaining sum from the pic)
Continued.....
p-q cannot be equal to 0
2a + (p+q-1)d=0
Now,for Sp+q, put n=p+q
Sp+q=p+q/2 [2a+(p+q-1)d]
=p+q/2 ×0
Sp+q=0
Hence it is proved
To prove : Sp+q=0
Formula: Sn=n/2 [2a+(n-1)d]
(copy the remaining sum from the pic)
Continued.....
p-q cannot be equal to 0
2a + (p+q-1)d=0
Now,for Sp+q, put n=p+q
Sp+q=p+q/2 [2a+(p+q-1)d]
=p+q/2 ×0
Sp+q=0
Hence it is proved
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