Question
Download Solution PDFनिम्नलिखित में से कौन सा कथन सही है?
I. 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 का मान 4840 है।
II.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
I. 100 2 - 99 2 + 98 2 - 97 2 + 96 2 - 95 2 + 94 2 - 93 2 + ...... + 22 2 - 21 2 का मान 4840 है।
द्वितीय. का मान है
प्रयुक्त अवधारणा:
ए, (ए + डी), (ए + 2 डी), ....., एल एक अंकगणितीय प्रगति है जिसमें पहला पद ए और सामान्य अंतर डी है। (एल एनवां पद है)
पदों की संख्या, N = (L - A)/D + 1
सभी पदों का योग = (A + L)/2 × N
गणना:
द्वितीय. अवधारणा के अनुसार,
100 2 - 99 2 + 98 2 - 97 2 + 96 2 - 95 2 + 94 2 - 93 2 + ...... + 222 - 21 2
(100 + 99) (100 - 99) + (98 + 97)(98 - 97)+...........(22 + 21)(22 - 21)
तो, श्रृंखला होगी
100 + 99 + 98 + 97 ................................................... ..22+21.
पहला पद 100 है और अंतिम 21 है, अंतर 1 है।
योग = (100 + 21) × 80/2 = 121 × 40 = 4840
द्वितीय.
∴ केवल I सत्य है।
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