Question

what is the answer for this? ​

Answer 1

Answer:

4/25 or 0.16

Step-by-step explanation:

(1/5*6) + (1/6*7) + (1/7*8)...+(1/24*25)

=>(6-5/5*6) + (7-6/6*7) + (8-7/7*8)....

=>(6-5/5*6) + (7-6/6*7) + (8-7/7*8)....+ (25-24/24*25)

=>(6-5/5*6) + (7-6/6*7) + (8-7/7*8)....+ (25-24/24*25)=>(6/5*6 - 5/5*6) + (7/6*7 - 6/6*7) + (8/7*8 - 8/7*8) +...+(25/24*25 - 24/24*25)

=>(1/5 - 1/6) + (1/6 - 1/7) + (1/7 - 1/8)+....+(1/24 - 1/25)

=>1/5 - 1/25

[as rest of the terms cancel out]

=>4/25 or 0.16

Answer 2

Question:

Find the value of given series;

1/5•6 + 1/6•7 + 1/7•8 + .........+ 1/24•25

Answer:

The required value of the given series is 4/25.

Solution:

Let the given series be "S".

Thus, we have;

=> S = 1/5•6 + 1/6•7 + 1/7•8 +..........

............ + 1/24•25

=> S = (6-5)/5•6 + (7-6)/6•7

+ (8-7)/7•8 + ....…...+ (25-24)/24•25

=> S = (1/5 - 1/6) + (1/6 - 1/7)

+ (1/7 - 1/8) + .......+ (1/24 - 1/25)

=> S = 1/5 - 1/25

=> S = (5 - 1)/25

=> S = 4/25

Hence,

The required value of the given series is 4/25 .