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CBSE Class 12-commerce Answered

if s1, s2, s3........sm are the sum of n terms of m AP's whose first terms are 1, 2.3..........m and common differences are 1, 3,5..........(2m-1), then show that s1+s2+s3........sm= mn/2 (mn+1)
Asked by rushabhjain.avv | 20 Nov, 2018, 10:51: AM
answered-by-expert Expert Answer
Let S = S1 + S2 + .......................+Sm
begin mathsize 12px style S subscript 1 equals n over 2 open square brackets 2 plus left parenthesis n minus 1 right parenthesis close square brackets
S subscript 2 space equals space n over 2 left square bracket 4 plus left parenthesis n minus 1 right parenthesis 3 right square bracket
S subscript 3 space equals space n over 2 left square bracket 6 plus open parentheses n minus 1 close parentheses 5 right square bracket
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S subscript m space equals space n over 2 open square brackets 2 m plus left parenthesis n minus 1 right parenthesis left parenthesis 2 m minus 1 right parenthesis close square brackets

H e n c e space space S space equals space n over 2 left square bracket 2 plus 4 plus 6.........2 m right square bracket space plus n over 2 open parentheses n minus 1 close parentheses left square bracket space space 1 plus 3 plus 5........ left parenthesis 2 m minus 1 right parenthesis space right square bracket
e a c h space t e r m space i n space left square bracket space right square bracket space a r e space i n space A. P space o f space m space n u m b e r s
H e n c e space S space equals space n over 2 open curly brackets m over 2 open square brackets 4 plus open parentheses m minus 1 close parentheses 2 close square brackets space plus space left parenthesis n minus 1 right parenthesis m over 2 open square brackets 2 plus open parentheses m minus 1 close parentheses 2 close square brackets close curly brackets space equals space fraction numerator m n over denominator 2 end fraction open square brackets m n plus 1 close square brackets end style
Answered by Thiyagarajan K | 21 Nov, 2018, 10:46: PM
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