Best approximation for y is

y=\(\frac{1}{2}−\frac{1}{3}+\frac{1}{6}−\frac{1}{10}+\frac{1}{12}−\frac{1}{14}+\frac{1}{16}\)

Best approximation for y is

A. 0.1
B. 0.31
C. 0.35
D. 0.4
E. 0.6

y=\(\frac{1}{2}−\frac{1}{3}+\frac{1}{6}−\frac{1}{10}+\frac{1}{12}−\frac{1}{14}+\frac{1}{16}\)
= \(\frac{1}{6}+\frac{1}{6}−\frac{1}{10}+\frac{1}{12}−\frac{1}{14}+\frac{1}{16}\)
= \(\frac{1}{3}−\frac{1}{10}+\frac{1}{12}−\frac{1}{14}+\frac{1}{16}\)
= \(\frac{1}{3}−\frac{1}{60}−\frac{1}{112}\)

As \(\frac{1}{10}-\frac{1}{12}=\frac{1}{60}\) and \(\frac{1}{14}-\frac{1}{16}=\frac{1}{112}\)
Above both values make a difference in hundredth position only.

Hence among values less than 0.33 B is nearer.

Answer B.

solve for given expression


IMO B ; 0.31

y=1/2−1/3+1/6−1/10+1/12−1/14+1/16
Best approximation for y is

A. 0.1
B. 0.31
C. 0.35
D. 0.4
E. 0.6

23/48 - 12/70=0.307
It's about0.31
So is closed to option B

Posted from my mobile device

My best approximation for the addition is 0.31

the first 3 fractions lead to 0

-1/10+1/12-1/14+1/16
cant give ending of /10 therefore 0.1,0.4, and 0.6 is out

now left with 0.31 and 0.35
I chose the ending with 1 because it seems like.
Therefore, B

common denominator for (1/2−1/3+1/6−1/10+1/12) is 60:
60•(1/2−1/3+1/6−1/10+1/12)/60=(30-20-10-6+5)/60=19/60
y=19/60-1/14+1/16=~20/60-1/15+1/15<~1/3=0.31

Answer (B)

Y= \(\frac{1}{2}–\frac{1}{3}+\frac{1}{6}–\frac{1}{10}+\frac{1}{12}–\frac{1}{14}+\frac{1}{16}\)=

=\(\frac{1}{2}–\frac{1}{3}+(\frac{1}{2}–\frac{1}{3})—\frac{1}{10}+(\frac{1}{3}–\frac{1}{4})—(\frac{1}{14}–\frac{1}{16}\)=

= \(\frac{1}{2}–\frac{1}{3}+\frac{1}{2}–\frac{1}{3}–\frac{1}{10}+\frac{1}{3}–\frac{1}{4}–(\frac{1}{14}–\frac{1}{16})\)=

\(1–\frac{1}{3}–\frac{1}{10}–\frac{1}{4}–\frac{(16–14)}{(14*16)}\)=

\(1–0.(3)—0.1–0.25–(\frac{1}{112})\)=

= \(0.65–0.(3)—\frac{1}{112}\)= \(0.32–\frac{1}{112}\)

Let’s simplify \(\frac{1}{112}\) :
—> it is less than \(\frac{1}{100}\)=0.01

—> 0.32–0.01= 0.31

The answer is B.

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