(C) n=0, 2, 4 im from the first ter...
Question

# (C) n=0, 2, 4 im from the first term to the kth term of the arithmetic sequence with the first term unity and Q.3 Let S be the sum from the first term to the kth terme common difference 1. The equals k=1 200 99 19 19 100

JEE/Engineering Exams
Maths
Solution
105
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( begin{aligned} sum_{k=1}^{100}left(frac{1}{s_{k}}right)=frac{1}{1}+frac{1}{1+2}+frac{1}{1+3}+cdots+frac{1}{k-10} &=sum_{k=1}^{100} frac{1}{left(frac{k(k+1)}{2}right)} =& 2 sum_{k=1}^{100}left(frac{(k+1)-(k)}{k(k+1)}right) =& 2 sum_{k=1}^{100}left(frac{1}{k}-frac{1}{k+1}right) text { for } k=1 & frac{1}{1}-frac{1}{2} k=2 & frac{1}{2}=frac{1}{3} k=3 & frac{1}{3}-frac{1}{4}- k=100 & frac{1}{100}-frac{1}{101} therefore & sum_{k=1}^{100}left(frac{1}{5}right)=2left(1-frac{1}{101}right)=frac{200}{101} end{aligned} )