Question

the sum of series: 45*45-43*43+44*44-42*42+43*43-41*41+42*42-40*40+.....till 15 terms

Answer 1

Answer:

45*45  + 44*44 - 37*37   = 2592

Explanation:

Given series is -

45*45 - 43*43 + 44*44 - 42*42 + 43*43 - 41*41 + 42*42  - 40*40 ....... upto 15 terms.

First term is 45*45

Second term is 2 less than first term that is 45-2 = 43

So, Second terms is 43*43

next term is one more than previous term that is 43 + 1 = 44

Third term = 44*44

Sign change alternate + , - , + , -  ....

Now we follow the same pattern

Series is :

45*45 - 43*43 + 44*44 - 42*42 + 43*43 - 41*41 + 42*42  - 40*40 + 41*41 - 39*39 + 40*40 - 38*38 + 39*39 - 37*37 + 38*38  

= 45*45 + 44*44 - 37*37

= 2592

Sum of the series  = 2592

That's the final answer.

Answer 2

Step-by-step explanation:

2592......................