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Question Number 212325 by MASANJAJJ last updated on 10/Oct/24

show that 1+(√(2 ))+2+..........+32(√(2 )) is 63(√2) +63

showthat1+2+2+..........+322is632+63

Answered by Ghisom last updated on 10/Oct/24

Σ_(k=0) ^n a^k =((a^(n+1) −1)/(a−1)) Σ_(k=0) ^(11) ((√2))^k =((((√2))^(12) −1)/( (√2)−1))=((64−1)/( (√2)−1))=63(1+(√2))

∑nk=0ak=an+1−1a−1∑11k=0(2)k=(2)12−12−1=64−12−1=63(1+2)

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