Question

Find the sum of series 45²-43²+44²-42²+43²-41²......to the 30 terms

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Answer 1

Answer:

HII MATE

HERE'S THE ANSWER

Step-by-step explanation:

The last 2 terms of series are: (45-15+1)²= 31² and -(43-15+1)²= -29²

Some of the components of the sum is cleared (from 43² to 31²), and will be following:

45² + 44² - 30² - 29² = 2220.

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Answer 2

• The sum of given series upto 30 terms is equal to 2220 .

To Find :- The sum of series :- 45²- 43² + 44²- 42² + 43²- 41² _____ upto 30 terms ?

Solution :-

→ 45² - 43² + 44² - 42² + 43² - 41² _____ 30 terms

So,

→ 15 positive terms are :- 45² + 44² + 43² + 42²+ ______ + 31²

→ 15 negative terms are :- -43² -42² -41² -40² _________ -29²

as we can see that, positive square from 43 upto square of 31 will be cancel with negative terms .

then,

→ (45² + 44² + 43² + 42²+ ______ + 31²) + (-43² -42² -41² -40² _________ -29²)

→ 45² + 44² + 43² - 43² + 42² - 42² ________ + 31² - 31² - 30² - 29²

→ 45² + 44² - 30² - 29²

→ 2025 + 1936 - 900 - 841

→ 3961 - 1741

→ 2220 (Ans.)

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