The expression (1+3+5+ ldots ldots .+99/2+4+6+ ldots . .+100) when simplified, reduces to the fraction

Question

The expression (1+3+5+ ldots ldots .+99/2+4+6+ ldots . .+100) when simplified, reduces to the fraction (A) (49/50) (B) (50/51) (C) (99/100) (D) (100/101)

Tardigrade Admin · Accepted Answer

S N =502 ; S D =(2 ⋅ 50 ⋅ 51/2)=50 ⋅ 51 ⇒ ( n / D )=(50/51)

Q. The expression $\frac{1 + 3 + 5 + \dots\dots . + 99}{2 + 4 + 6 + \dots .. + 100}$ when simplified, reduces to the fraction

$\frac{49}{50}$

$\frac{50}{51}$

$\frac{99}{100}$

$\frac{100}{101}$

$S_{N} = 5 0^{2}; S_{D} = \frac{2 \cdot 50 \cdot 51}{2} = 50 \cdot 51 \Rightarrow \frac{n}{D} = \frac{50}{51}$

Q. The expression 2+4+6+…..+1001+3+5+…….+99​ when simplified, reduces to the fraction

5049​

5150​

10099​

101100​