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1,6,7,13,20.....Find the sum of first 52 terms!

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TCS Other Question

there are 18 horses..winning prob of 1st horse is 1/6,2nd=1/6 and 3rd is 1/7.. no possibility of
tie.. find the chances that one of these will win the race.
if f(1)=4,f(x+y)=f(x)+f(y)+7xy+2, for x>0,y>0 find f(2)+f(5)=?