Question

1
19. Find the value of (1/2×3)+(1/3×4)+(1/4×5)+(1/5×6)+...+(1/9×10)​

Answer 1

Answer:

Infinity

Step-by-step explanation:

In these summations , we first write the nth term

Notice here the nth term will be 1/(n)(n+1)

It can be written as (n+1)−n/(n)(n+1)

=>1/n−1/(n+1)

Now when you take summations from n=1 to infinity, you can observe cancellation of terms

T1 =1/1−1/2

T2 =1/2−1/3

T3 =1/3−1/4

And so on till infinity

As by calculation we will be left with 1 - 1/infinity the negative term will be approximately zero therefore the answer will be 1

Hope this helps!

Answer 2

Answer:

1.39

Step-by-step explanation:

=(1/2×3)+(1/3×4)+(1/4×5)+(1/5×6)+(1/9×10)​

=3/2+4/3+5/4+6/5+10/9

= lcm of 2,3,4,5,9=1080

=(1080/2)+(1080/3)+(1080/4)+(1080/5)+(1080/9) / 1080

=540+360+270+216+120/1080

=1506/1080

=1.39 is the answer  by dividing 1506/1080

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